2.6 - Section 2.6 Inverses Definition: For an nXn matrix A,...

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Section 2.6 Inverses Definition : For an nXn matrix A, A -1 , read "A inverse " is the matrix such that A A -1 = I n A -1 A = I n Example: Verify that if 13 11 A  =   then 1 3 1 44 A = 3 1 1 0 0 1  =   3 1 1 0 0 1 =
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To find inverses of 2X2 matrices, 1 1 ab if A then cd db A ca ad bc  =   = Example: 43 11 A = Find A -1 . 1 13 1 14 4(1) (3)( 1) A = −− 3 1 1 77 14 14 7 ==
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For larger than 2X2 matrices, reduce 1 A It oI A   Why ? From the previous section, we learned to solve AX = B by reducing A Bt o I X Since AA -1 = I, it's like the part of B is played by I and the part of X is played by A -1 . Example : 100 210 341 A  = Find A -1 .
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100 210 010 341 001    21 31 2 3 R R R R 1 00 041301 32 4 R R 1 0 0 0 1 0 5 41 1 10 0 54 1 A =− Note: If we can't get I on the left, then A has no inverse i.e. it's not invertible .
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If we know A -1 , then we can easily solve AX = B because multiplying on each side by A -1 gives us X = A -1 B. Example: Solve 1 12 3 5 21 2 34 2 x xx x = +=
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This note was uploaded on 10/16/2009 for the course MATH 1114 at Virginia Tech.

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2.6 - Section 2.6 Inverses Definition: For an nXn matrix A,...

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