jerri-2-5 - Section 2.5 The Matrix Equation AX = B Recall...

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Section 2.5 The Matrix Equation AX = B Recall we just worked with Ax = b where A was a matrix, x & b were vectors. For the Matrix Equation AX = B, A is the mXn matrix of coefficients X is the nXq matrix of solutions B is the mXq matrix of constants Column form of a matrix Default is 123 [ , , ,..., ] n A AA A A = unless specified otherwise Example 1 1 2 3 A   =  2 4 5 6 A = 3 7 8 9 A =
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(a) Display the matrix A. 147 258 369 A = (b) Display the matrix A=[A 3 , A 2 , A 2 ] 744 855 966 A   =  (c) Display the matrix A=[A 1 - A 2 , A 3 ] (Note that the columns are separated by commas.) 12 14 25 36 AA   −=  3 3 3 =− 37 38 39 A
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Theorem: Let A be an mXn matrix and B be an nXp matrix such that B=[B 1 , B 2 , . .., B p ]. Then in column form, AB = [AB 1 , AB 2 , . .., AB p ] Example 123 12 3 [, , ] 34 01 1 ,, 31 2 If A and B B B B where B B B  ==
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This note was uploaded on 11/11/2008 for the course MATH 1114 taught by Professor Jhengland during the Fall '08 term at Virginia Tech.

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jerri-2-5 - Section 2.5 The Matrix Equation AX = B Recall...

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