l4 - Math 20F Linear Algebra Lecture 4: 1.4 Matrix...

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Unformatted text preview: Math 20F Linear Algebra Lecture 4: 1.4 Matrix Multiplication and the Matrix Equation. A = a 11 a 12 ... a 1 n a 21 a 22 ... a in . . . a m 1 a m 2 ... a mn , x = x 1 x 2 . . . x n , A is an m n matrix and x R n . Define the product A x R m by A x = x 1 a 11 a 21 . . . a m 1 + x 2 a 12 a 22 . . . a m 2 + + x n a 1 n a 2 n . . . a mn = x 1 a 1 + x 2 a 2 + + x n a m Then Matrix multiplication the matrix A defines a mapping from R n to R m . Notice that A x = a 11 x 1 + a 12 x 2 + ... + a 1 n x n a 21 x 1 + a 22 x 2 + ... + a 2 n x n . . . a m 1 x 1 + a m 2 x 2 + ... + a mn x n . The j th term down is obtained by dotting the j th row of A with x . Ex 1- 4 3 2 5 7- 6 = 7 1 3 +- 6 - 4 2 5 = 7 21 + 24- 12- 30 = 31 9- 30 ....
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l4 - Math 20F Linear Algebra Lecture 4: 1.4 Matrix...

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