l_notes31 - Lecture XXXI Linear Equation Systems As we saw...

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Unformatted text preview: Lecture XXXI Linear Equation Systems As we saw in the previous lecture, we can multiply m n matrices by column n-vectors. Consider the rows of an m n matrix A to be n-vectors: r 1 c 1 r 1 C r 2 . . . , C = c 2 . . . then AC = r 2 C . . A = . C r m c n r m For example, if 7 1 2 1 27 22 , C = , then AC = 9 A = 4 0 3 2 We can use multiplication by a column vector to solve equation systems. An m n equation system has the form a 11 x 1 + a 12 x 2 + + a 1 n x n = d 1 a 21 x 1 + a 22 x 2 + + a 2 n x n = d 2 a m 1 x 1 + a m 2 x 2 + + a mn x n = d m This system has m equations and n unknowns: x 1 , x 2 , , x n . An example of a 2 3 system is 4 x 1 + 3 x 2 x 3 = 1 x 1 x...
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l_notes31 - Lecture XXXI Linear Equation Systems As we saw...

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