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lecture_3- Matrix Multiplication Part 1

# lecture_3- Matrix Multiplication Part 1 - MA 265 LECTURE...

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MA 265 LECTURE NOTES: FRIDAY, JANUARY 11 Matrices (cont’d) Review of Definitions. Recall that the coefficients in a system of m linear equation in n unknowns 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 correspond to an m × n matrix: A = a 11 a 12 ... a 1 n a 21 a 22 ... a 2 n . . . . . . . . . . . . a m 1 a m 2 ... a mn . Examples. Consider the following two matrices: A = bracketleftbigg 1 2 3 - 1 0 1 bracketrightbigg and B = bracketleftbigg 1 + i 4 i 2 - 3 i - 3 bracketrightbigg . Since A 2 rows and 3 columns, it is a 2 × 3 matrix. Since B has 2 rows and 2 columns, it is a 2 × 2 matrix. Note that the entries can either be real or complex numbers. Matrix Operations Matrix Addition. Say that A and B are both m × n matrices. Then we define the addition as the m × n matrix A = bracketleftbig a ij bracketrightbig , B = bracketleftbig b ij bracketrightbig = A + B = bracketleftbig a ij + b ij bracketrightbig . Note that addition can only be defined when A and B have both the same number of rows m and the same number of columns n . Example. Consider the following 2 × 3 matrices: A = bracketleftbigg 1 - 2 3 2 - 1 4 bracketrightbigg and B = bracketleftbigg 0 2 1 1 3 - 4 bracketrightbigg .

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lecture_3- Matrix Multiplication Part 1 - MA 265 LECTURE...

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