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• Vector and complex variables
  It has two rows and two columns. In other words, this is a $2 \times 2$ matrix. The following combination of $A$ and $B$ is called the ''augmented matrix'' of the system:
  113 KB (18,750 words) - 02:33, 10 December 2018
• Transformations
  It has two rows and two columns. In other words, this is a $2 \times 2$ matrix. This is a $2 \times 1$ matrix.
  46 KB (7,625 words) - 13:08, 26 February 2018
• Functions of several variables: derivatives and integrals
  '''Theorem (Algebra of Derivatives).''' Suppose $f$ and $g$ are differentiable at $X=A$. Then, It has two rows and two columns. In other words, this is a $2 \times 2$ matrix.
  42 KB (6,904 words) - 15:15, 30 October 2017
• Matrices: part 2
  ==Properties of matrix operations== The properties of matrix multiplication are very much like the ones for numbers.
  14 KB (2,302 words) - 19:46, 27 January 2013
• Linear functions in Euclidean space
  There is another connection to linear algebra. The set <center>$dy = f’(a)(dx)$, where $f’(a)$ is a matrix.</center>
  23 KB (3,893 words) - 04:43, 15 February 2013
• Matrices: part 1
  Solve by substitution or by using the "[[augmented matrix]]": *The first matrix is $2 \times 2$: the coefficients of $x,y$.
  8 KB (1,275 words) - 14:18, 9 September 2011
• Metric complexes
  ...obvious that only the way the cells are attached to each other affects the matrix of the boundary operator (and the exterior derivative): In linear algebra, we learn how an inner product adds geometry to a vector space. We choose a
  35 KB (5,871 words) - 22:43, 7 April 2016
• Metric tensor
  ...obvious that only the way the cells are attached to each other affects the matrix of the exterior derivative: However, does this algebra imply concavity? Not without assuming that the intervals have equal lengths
  42 KB (7,131 words) - 17:31, 30 November 2015
• Systems of ODEs
  ...''Hessian matrix'' (discussed in Chapter 18) of $G$. It is the $2\times 2$ matrix of the four partial derivatives of $G$: ...linear function $F$. As such, it is given by a matrix and is evaluated via matrix multiplication:
  63 KB (10,958 words) - 14:27, 24 November 2018
• Linear operators: part 2
  We already know that ''each matrix give rise to a linear operator''. ==How to find a matrix for a linear operator==
  8 KB (1,375 words) - 19:58, 10 September 2011
• PageRank as a solution of a matrix equation
  be the vector of ranks at time $t$. Then, in [[matrix]] notation: where the matrix $M$ is defined as
  5 KB (811 words) - 18:36, 28 November 2012
• Algebra on graphs
  ...is via its ''incidence matrix''<!--\index{incidence matrix}-->, i.e., the matrix with a $1$ in the $(i,j)$-entry if the graph contains edge $ij$ and $0$s el <!--75-->[[image:TopologicalFigure8 and cycle algebra.png| center]]
  36 KB (6,177 words) - 02:47, 21 February 2016
• Determinants of linear operators
  ==How to determine that a matrix is invertible?== Given a matrix or a linear operator $A$, it is either singular or non-singular:
  19 KB (3,177 words) - 18:59, 10 October 2011
• Linear operators: part 3
  ...e left refers to the inverse of the operator while on the right it's about matrix inverse. Note: This is a matrix equation.
  10 KB (1,612 words) - 14:25, 16 October 2013
• Computing homology
  Recall that given a [[cell complex]] $K$, a $k$-[[the algebra of chains|chain]] is a "formal" [[linear combination]] of finitely many ori '''Linear algebra problem.''' Find real numbers (turns out integers) $u, v$, and $w$ such tha
  26 KB (4,370 words) - 21:55, 10 January 2014
• Homology groups of graphs
  ==The algebra of plumbing== ...pursue this analysis via a certain kind of ''algebra''. We introduce this algebra with the following metaphor:
  28 KB (4,685 words) - 17:25, 28 November 2015
• Social choice
  We will look into the first two options as they are subject to the algebra we have developed in this chapter. ==The algebra of vote aggregation==
  47 KB (8,030 words) - 18:48, 30 November 2015
• Vector spaces: introduction
  ==Real numbers and their algebra== Where does this algebra:
  14 KB (2,238 words) - 17:38, 5 September 2011
• Eigenvalues and eigenvectors of linear operators
  Given a basis $\{v_1,v_2\}$, define a linear operator with matrix $A = \left[ If this is not the standard basis, then the matrix is not ''diagonal''.
  12 KB (1,971 words) - 01:09, 12 October 2011
• Linear algebra: exercises
  These are exercises for [[Linear algebra: course]]. [[Linear Algebra by Messer]]
  5 KB (833 words) - 13:36, 14 March 2018
• Inner product
  ...\cdot, \cdot >$ on an $n$-dimensional vector space $V$ can be computed via matrix multiplication where $Q$ is a positive definite, symmetric $n \times n$ matrix.
  4 KB (749 words) - 20:12, 1 May 2013
• Matrices as functions
  Turns out, this is [[matrix product]]! It is called a ''matrix representation'' of this function, $F$. But, if we do have a matrix, we can always understand it as a function, example:
  13 KB (2,187 words) - 22:17, 9 September 2011
• Functions
  ...ften given by ''formulas''. In that case, the above issue is resolved with algebra. ...t: $A$ depends on $w$ only. What is this function? With more middle school algebra, we make this function explicit:
  151 KB (25,679 words) - 17:09, 20 February 2019
• The algebra of oriented cells
  With the algebra we have learned, we can easily conclude the following about the homology of
  36 KB (6,395 words) - 14:09, 1 December 2015
• Homotopy
  as quotients of the maps of chains. However, in comparison, where is the algebra in these homotopy ''groups''? <!--200-->[[image:algebra of loops.png|center]]
  46 KB (7,846 words) - 02:47, 30 November 2015
• Linear operators: part 4
  '''Lesson:''' Linear algebra reveals the ''[[topology]]'' of the graph. ...ifferentiation \hspace{3pt}} \colon {\bf P} \rightarrow {\bf P}$. Find the matrix.
  13 KB (2,067 words) - 01:11, 12 September 2011
• Simplicial homology
  ...clear that another choice of cells' orientations will produce a different algebra of chains... but the same homology groups<!--\index{homology groups}-->! In ==The algebra of oriented chains==
  31 KB (5,170 words) - 13:44, 1 December 2015
• Duality: forms as cochains
  Linear algebra helps one appreciate this seemingly trivial relation. The answer is given b ...cating what $0, -\alpha \in V^*$ are, and then refer to theorems of linear algebra.
  29 KB (4,540 words) - 13:42, 14 March 2016
• Cohomology
  Linear algebra helps one appreciate this seemingly trivial relation. Indeed, the answer is ...cating what $0, -\alpha \in V^*$ are, and then refer to theorems of linear algebra.
  45 KB (6,860 words) - 16:46, 30 November 2015
• Topology of graphs
  ...is via its ''incidence matrix''<!--\index{incidence matrix}-->, i.e., the matrix with a $1$ in the $ij$ position if the graph contains edge $ij$ and $0$s el It is time now to start to recognize the ''need for algebra'' in topology.
  25 KB (4,214 words) - 16:08, 28 November 2015
• Calculus Illustrated
  6 The algebra of exponents 11 The algebra of sums and differences
  16 KB (1,933 words) - 19:50, 28 June 2021
• Test
  #[[Topology vs algebra vs geometry]] #[[Algebra of differential forms]]
  16 KB (2,139 words) - 23:01, 9 February 2015
• Forms in Euclidean spaces
  In order to simplify things, we utilize what we know about the ''algebra'' of directions on ${\bf R}$: the direction from $n$ to $n+1$ is the opposi Both approaches rely on ''the algebra of the Euclidean space''.
  44 KB (7,778 words) - 23:32, 24 April 2015
• College Algebra -- Fall 2016
  '''MTH 130 College Algebra.''' 3 hrs. Polynomial, rational, exponential, and logarithmic functions. Gr *Prerequisites: solid algebra skills, some knowledge of Cartesian coordinates, familiarity with basic fun
  10 KB (1,078 words) - 19:07, 16 December 2016
• Modeling with discrete exterior calculus
  ...geneous case, so for the purposes of speed of the program,the conductivity matrix was replaced with a constant $k=0.6$. ...model is isotropic. In order to do this, we take [[level curve]]s of this matrix at varying times and observe the shape of these curves. We began by taking
  31 KB (5,254 words) - 17:57, 21 July 2012
• Applied Topology and Geometry
  #[[Topology vs algebra vs geometry]] #[[Algebra of differential forms]]
  16 KB (2,088 words) - 16:37, 29 November 2014
• Homotopy and homotopy equivalence
  as quotients of the maps of chains. However, in comparison, where is the algebra in these homotopy ''groups''? [[image:algebra of loops.png|center]]
  45 KB (7,738 words) - 15:18, 24 October 2015
• The algebra of cubical cells
  ...appears twice, it is canceled. The computation is carried out as if we do algebra with ''binary arithmetic''<!--\index{binary arithmetic}-->. That's why we c With the algebra we have learned, we can easily conclude the following about these cycles:
  46 KB (7,844 words) - 12:50, 30 March 2016
• Simplicial complexes and maps
  ==The algebra of oriented chains== Up to this point, the development of the algebra of chains follows the same path as in the case of oriented ''cubical'' comp
  27 KB (4,625 words) - 12:52, 30 March 2016
• College Algebra by Ratti and McWaters
  ''College Algebra'', 2/E by J. S. Ratti and Marcus S. McWaters Used it for [[College Algebra -- Fall 2011]], see also [[College algebra: course]]. It's better than many others I've seen.
  2 KB (269 words) - 18:53, 16 November 2011
• Homology in dimension 2
  Recall that given a [[cell complex]] $K$, a $k$-[[the algebra of chains|chain]] is a "formal" [[linear combination]] of finitely many ori is represented by a $6 \times 3$ [[matrix of a linear operator|matrix]].
  8 KB (1,318 words) - 18:42, 27 August 2015
• Cochains on graphs
  ==The algebra of plumbing, continued== We introduce more algebra with the familiar metaphor:
  15 KB (2,523 words) - 18:08, 28 November 2015
• Calculus on graphs
  ==The algebra of plumbing, continued== We introduce more algebra with the familiar metaphor.
  16 KB (2,578 words) - 00:14, 18 February 2016
• Cochain complexes and cohomology
  ...ollowing is very similar to the continuous case (why? because the [[linear algebra]] is the same). ...[[linear operator]], which is its $4 \times 4$ [[Linear operators: part 2|matrix]].
  17 KB (2,592 words) - 14:38, 14 April 2013
• The algebra of oriented cubes
  With the algebra we have learned, we can easily conclude the following about these cycles:
  32 KB (5,480 words) - 02:23, 26 March 2016
• Maps of graphs
  We can now move on to algebra. '''Exercise.''' Find the matrix of the chain map of a graph map that shifts by one edge a graph of $n$ edge
  29 KB (5,042 words) - 17:57, 28 November 2015
• MATLAB
  ...gineers (I mean <em>engineers</em>, not computer programmers) to explore [[matrix]] models interactively, then save their work as scripts - you were never me ...e mathematical chops to rearrange your problem into something solvable via matrix transformations, you can probably write it quickly and elegantly in Matlab
  4 KB (548 words) - 14:55, 9 October 2010
• How to compute Betti numbers
  ...lls. The coefficients of these linear combinations form the columns of the matrix. As such it is the solution of the matrix equation:
  5 KB (890 words) - 14:47, 24 August 2014
• Chain maps
  We can now move on to algebra. These three identities immediately give us the three columns of the matrix of the linear operator $f_0:C_0(K)\to C_0(L)$, or $f_0:{\bf R}^3\to {\bf R}
  47 KB (8,115 words) - 16:19, 20 July 2016
• Elementary Linear Algebra -- Spring 2018
  '''MTH 329 – Elementary Linear Algebra.''' Systems of linear equations, matrices and determinants, vector spaces, *Prerequisites: excellent algebra skills, working knowledge of basic Euclidean geometry, good understanding o
  4 KB (573 words) - 13:07, 7 April 2018
• Elementary Linear Algebra -- Spring 2019
  '''MTH 329 – Elementary Linear Algebra.''' Systems of linear equations, matrices and determinants, vector spaces, *Prerequisites: excellent algebra skills, working knowledge of basic Euclidean geometry, good understanding o
  3 KB (321 words) - 21:06, 19 February 2019
• Computational Homology by Kaczynski, Mischaikow, Mrozek
  ...ot easy to handle for a novice. In fact, a graduate level course in modern algebra, as well as some point-set topology, seems to be required for the student t **2.2 The Algebra of Cubical Sets
  5 KB (616 words) - 14:03, 6 October 2016
• Preview of calculus: part 2
  '''Algebra:''' ...th even a bit more complicated functions we wouldn't be able to handle the algebra. Calculus will help...
  19 KB (2,850 words) - 15:04, 19 March 2011
• Basic Linear Algebra by Blyth and Robertson
  ''Basic Linear Algebra'' by Blyth and Robertson [[Linear algebra: course]]
  814 bytes (107 words) - 20:33, 6 March 2016
• Linear algebra: final
  Final exam for [[Linear algebra: course]] ...of an $n\times n$ matrix. (b) Find the determinant of an upper-triangular matrix (all entries below the main diagonal are $0$). (c) Is the determinant a lin
  2 KB (376 words) - 20:27, 13 June 2011
• Linear algebra: test 2
  Test 2 for [[Linear algebra: course]] #Suppose $A$ is an invertible matrix. What is $(A^{m})^{-1}?$
  4 KB (583 words) - 01:13, 12 October 2011
• Change of variables in vector spaces
  In [[linear algebra]], this is identical to ''change of basis''. This conversion is provided by a [[linear operator]] (and a matrix):
  2 KB (473 words) - 02:25, 22 August 2013
• Cubical complex
  As before, the big picture of the algebra of chains and their boundaries is given by the ''chain complex of the cubic Now using only algebra, we deduce:
  29 KB (4,800 words) - 13:41, 1 December 2015
• Cubical complexes
  As before, the big picture of the algebra of chains and their boundaries is given by the ''chain complex of the cubic Now using only algebra, we deduce:
  20 KB (3,319 words) - 14:18, 18 February 2016
• Linear operators: part 5
  ...the image ${\rm im \hspace{3pt}}A$ is spanned by the column vectors of the matrix (called the ''column space''). that's the rank of the matrix. (equal to the number of linearly independent rows, exercise)
  11 KB (1,929 words) - 01:11, 12 September 2011
• Calculus exercises: part III
  ==Algebra and geometry== *Represent the system of linear equations as a matrix equation:
  46 KB (8,035 words) - 13:50, 15 March 2018
• Calculus is the dual of topology
  ...matrix of the [[exterior derivative]] is equal to the [[transpose]] of the matrix of the [[boundary operator]]! This means that we now know the exterior deri <center> calculus is built on top of topology with algebra. </center>
  2 KB (272 words) - 20:41, 13 February 2015
• How to compute homology
  ...lls. The coefficients of these linear combinations form the columns of the matrix. As such it is the solution of the matrix equation:
  6 KB (1,049 words) - 09:21, 3 September 2011
• Diagonalization of matrices
  And, the change of basis matrix is '''Easier:''' matrix $D$ of the operator $A$ with respect to $\{v_1,v_2\}$: $D = $ made of colum
  10 KB (1,529 words) - 03:39, 12 October 2011
• Rating votes
  ...ly is a function of matrices and the output a vector, over ${\bf Z}$. This matrix represents an election and its $(i,j)$-entry is the rating assigned by the *interchanging the ''columns'' in the matrix doesn't affect the outcome; $\\$
  9 KB (1,553 words) - 06:12, 22 June 2016
• Stochastic matrix
  A row (column) ''stochastic [[matrix]]'' is a square matrix each of whose rows (columns) consists of non-negative real numbers whose su Matrix $A=(a_{ij})$ is column stochastic if
  453 bytes (69 words) - 21:58, 27 August 2011
• The high contrast homology of a gray scale image
  ...ust ones of dimension (or co-dimension) $0$. This fact is reflected in the algebra presented above. Indeed we can compute the contrast as the life-spans (pers \begin{matrix}
  8 KB (1,196 words) - 13:29, 28 August 2015
• Linear operators: part 1
  {\rm function \hspace{3pt} notation} & {\rm matrix \hspace{3pt} notation} \\ {\rm compositions} & {\rm matrix \hspace{3pt} multiplication} \\
  13 KB (2,086 words) - 19:58, 27 January 2013
• Euler and Lefschetz numbers
  ...ar, counting cells in the definition is replaced with the following linear algebra. '''Proof.''' The proof will require a couple of facts from linear algebra.
  41 KB (7,169 words) - 14:00, 1 December 2015
• Higher order votes
  ...sional $m\times m\times n$-matrices with matrices as its values. Each such matrix represents an election and its $(i,j,k)$-entry is the score assigned by the We now use this terminology to restate what we know form algebra.
  41 KB (6,942 words) - 05:04, 22 June 2016
• Solving systems of linear equations
  *[[Reduced row echelon form]] of a matrix is unique. Now let's simplify the algebra:
  5 KB (802 words) - 01:38, 6 September 2011
• Links
  *[[Multilinear algebra]] #[[Calculus and algebra vs topology]]
  6 KB (998 words) - 12:40, 31 August 2015
• Discrete Calculus: Applied Analysis on Graphs for Computational Science by Grady and Polimeni
  ...e matrix of the [[exterior derivative]] is simply the [[transpose]] of the matrix of the [[boundary operator]]. The fact is well-known but I never saw the d <center>'''[[calculus / algebra = topology]].'''</center>
  11 KB (1,663 words) - 16:03, 26 November 2012
• Chain complexes
  ...and results can be found in the standard literature such as Hungerford, ''Algebra'' (Chapter IV). Now using only algebra, we deduce:
  33 KB (5,293 words) - 03:06, 31 March 2016
• Homology
  Now, cells are combined into ''[[the algebra of chains|chains]]''. For example, $P$ and $Q$ are $2$-chains consisting of One can define [[The algebra of chains|homology with arbitrary coefficients]], as long as it's a [[ring]
  8 KB (1,388 words) - 14:03, 1 June 2014
• Integration of differential forms of degree 2
  Let's recall what we mean by ''algebra of chains and cochains''. ...the matrix of the [[exterior derivative]] $d$ is the [[transpose]] of the matrix of the [[boundary operator]] $\partial$ :
  15 KB (2,341 words) - 20:53, 13 March 2013
• Review exercises
  '''Example:''' $A$ is [[singular matrix|singular]] iff 0 is an [[eigenvalue]]. Find the matrix of $T$.
  4 KB (677 words) - 17:31, 13 October 2011
• Linear Algebra -- Spring 2013 -- final exam
  ...t the set of all diagonal $n \times n$ matrices form a vector space. (b) A matrix is called upper-triangular if all entries below the main diagonal are equal #Find the inverse the matrix: \begin{equation*}A=\left[\begin{array}{cc}1 & 1 \\ 1 & 1\end{array}\right]
  2 KB (330 words) - 02:21, 7 May 2013
• Applied Topology and Geometry: preface
  ...topology require [[group theory: course|groups theory]] and even advanced algebra. For some chapters on differential forms the reader can benefit from a prio
  3 KB (409 words) - 15:46, 22 August 2015
• Parametric complexes
  ...*$! One can think of those left as the orthogonal complement in the linear algebra environment, $(\operatorname{Im}\,i_*^{n})^{\bot}$, or we can exclude the i We use the algebra of homology classes:
  45 KB (7,255 words) - 03:59, 29 November 2015
• Topology Illustrated -- Index
  *[[Fundamental Theorem of Algebra|Fundamental Theorem of Algebra]] *[[incidence matrix|incidence matrix]]
  16 KB (1,773 words) - 00:41, 17 February 2016
• Internal structure of a vector space: part 3
  Now form a system of linear equations based on (*). It's matrix is the [[transpose]] of the above: Consider the [[homogeneous system]] of linear equations with this matrix.
  14 KB (2,455 words) - 19:00, 7 September 2011
• Linear algebra: homework 1
  Next, find the matrix of $R_{\alpha},R_{\beta}$, multiply, show that this is $R_{\alpha+\beta}$. \right]$, then $R_{\alpha}$ is a $2 \times 2$ matrix?
  2 KB (427 words) - 03:30, 11 September 2011
• Geometry of Euclidean space
  $$< P, P > = < P', P >, {\rm \hspace{3pt} some \hspace{3pt} algebra...}$$ ...erms of their coordinates by putting these three vectors in a $3 \times 3$ matrix:
  21 KB (3,396 words) - 20:31, 10 August 2011
• Combinatorial cell maps
  ...and results can be found in the standard literature such as Hungerford, ''Algebra'' (Chapter IV). The topological setup above is now translated into algebra. From a cell map, we construct maps on the chain groups of the two cell com
  31 KB (5,330 words) - 22:14, 14 March 2016
• Discrete forms and cochains
  ...rmore, as we shall see, the transition from topology to calculus is just ''algebra''! These numbers form the matrix of $\partial ^0$, which is, as we see, the transpose of $\partial _1$:
  34 KB (5,619 words) - 16:00, 30 November 2015
• Dual space
  [[Linear algebra]] helps one appreciate this seemingly trivial relation. Indeed, the answer ...th indicating what $0, -\alpha \in V^*$ are. Refer to theorems of [[linear algebra]], such as the "[[Subspace Theorem]]".
  9 KB (1,390 words) - 16:14, 16 June 2014
• College Algebra by Sullivan
  R.2 Algebra Essentials 5.6 Complex Zeros: Fundamental Theorem of Algebra
  3 KB (349 words) - 16:29, 8 August 2013
• Perron–Frobenius theorem
  Suppose $A = (a_{ij})$ is an $n × n$ positive matrix: $a_{ij} > 0$ for $1 ≤ i, j ≤ n$. Then there is a real [[eigenvalue]] $ ...= (a_{ij})$ is an $n × n$ [[irreducible matrix|irreducible]] non-negative matrix: $a_{ij} \geq 0$ for $1 ≤ i, j ≤ n$. Then there is a positive real eige
  2 KB (239 words) - 15:08, 25 August 2011
• The topology of data
  *[[Homology and algebra]] ...sed program that can be run in the JPlex window that constructs a distance matrix from the point cloud. In order to compute the relative homology we set all
  9 KB (1,431 words) - 16:57, 20 February 2011
• Transpose
  Matrix $B=\{ b_{ij} \}$ is called the ''transpose'' of matrix $A=\{ a_{ij} \}$ when [[category:linear algebra]]
  177 bytes (29 words) - 15:26, 28 June 2012
• More metric complexes
  ...cells (open or closed) $\Sigma$ of $K$ as subsets of $|K|$ form a $\sigma$-algebra, i.e., a collection closed under the operations of complement, countable un '''Proposition.''' The matrix of the Hodge star operator $\star$ is diagonal with:
  21 KB (3,445 words) - 13:53, 19 February 2016
• Examples of differential forms
  where $f'(a)$ is a linear function (a matrix) and $u$ and $v$ are [[vectors]]. This follows from the fact that the deriv The RHS here should be read as either the fot product or as the product of a matrix and a vector.
  5 KB (959 words) - 13:15, 12 August 2015
• Geometric complexes
  ...n the set of all cells $\Sigma$ of $K$ as subsets of $|K|$ form a $\sigma$-algebra, i.e., a collection closed under the operations of complement, countable un '''Proposition.''' The matrix of the Hodge star operator $\star$ is diagonal with:
  20 KB (3,354 words) - 17:37, 30 November 2015
• Linear algebra: test 1
  Test 1 for [[Linear algebra: course]] (Note: the first term on the right hand side of the matrix equations is a vector and the second term is a point.)
  4 KB (538 words) - 20:28, 9 September 2011
• Contemporary Abstract Algebra by Gallian
  ''Contemporary Abstract Algebra'' by Joseph A. Gallian Used the book (twice) -- for [[Modern Algebra I -- Fall 2011]], see also [[Group theory: course]].
  5 KB (568 words) - 15:23, 16 November 2011
• Applied Calculus -- Spring 2015
  ...classes of functions, graph these functions, solve equations -- [[College Algebra -- Fall 2014]] **8.5 The Inverse of a Matrix
  9 KB (1,141 words) - 16:08, 26 April 2015
• ODEs
  Second, since complex $K$ has no algebra that we use, In fact, if we ignore the algebra of the $x$- and $y$-axis, we realize that our equation is a relation betwee
  47 KB (8,415 words) - 15:46, 1 December 2015
• Partial differential equations
  '''Exercise.''' What is the matrix of this ''linear'' transformation? ...s the difference: two with respect to $x$ and two with respect to $y$. The algebra that follows is identical to that we used for the heat equation in dimensio
  53 KB (9,682 words) - 23:19, 18 November 2018
• Linear algebra: midterm
  MATH 331 Linear Algebra .... Spring 2013 ......................... NAME_____________ #Represent the system of linear equation in problem #3 as a matrix equation.
  1 KB (217 words) - 20:45, 14 March 2013

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