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# Lecture7 - University of Toronto at Scarborough Department...

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University of Toronto at Scarborough Department of Computer & Mathematical Sciences MAT A23 Winter 2008 Lecture 7 Sophie Chrysostomou 1.4 Solving Systems of Linear Equations The Connection Between Linear Systems of Equations and Matrices Suppose that A = a 11 a 12 · · · a 1 n a 21 a 22 · · · a 2 n . . . . . . . . . . . . a m 1 a m 2 · · · a mn , x = x 1 x 2 . . . x n , b = b 1 b 2 . . . b m what is the meaning of A x = b ? definition 0.1. Suppose we have the linear system a 11 x 1 + a 12 x 2 + ... + a 1 n x n = b 1 a 21 x 1 + a 22 x 2 + ... + a 2 n x n = b 2 . . . . . . . . . . . . . . . . . . a m 1 x 1 + a m 2 x 2 + ... + a mn x n = b m This is equivalent to A x = b where A = a 11 a 12 · · · a 1 n a 21 a 22 · · · a 2 n . . . . . . . . . . . . a m 1 a m 2 · · · a mn , x = x 1 x 2 . . . x n , b = b 1 b 2 . . . b m 1

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A is called the coefficient matrix of the system and A = a 11 a 12 · · · a 1 n a 21 a 22
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