C__DOCUME~1_MAXWID~1_LOCALS~1_Temp_plugtmp-27_notes2-2

# C__DOCUME~1_MAXWID~1_LOCALS~1_Temp_plugtmp-27_notes2-2 -...

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SECTION 2.2 MATRIX INVERSES If the matrix A is square and there is a matrix C such that CA = AC = I , then A is called invertible and C is called the inverse of A , which we denote by A - 1 . A matrix that is not invertible is called singular . FACT. Products and transposes of invertible matrices are invertible. A bunch of algebra veriﬁes the rule on page 119 for 2 × 2 matrices. EXAMPLE. Find the inverse of " 1 - 2 3 - 4 # .

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To ﬁnd A - 1 in general, we need to solve AC = I . Unravel this to see that we need to
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Unformatted text preview: perform row operations on the matrix [ A I ] to produce [ I A-1 ]. It is a remarkable and remarkably useful fact that the three row operations can be performed using multiplication on the left by what are called elementary matrices . " 0 1 1 0 # " 1-2 3-4 # " 3 0 0 1 # " 1-2 3-4 # " 1 0 5 1 # " 1-2 3-4 # Use this to investigate the existence of A-1 . HOMEWORK: SECTION 2.2...
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## This note was uploaded on 04/15/2008 for the course M 340L taught by Professor Pavlovic during the Spring '08 term at University of Texas at Austin.

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C__DOCUME~1_MAXWID~1_LOCALS~1_Temp_plugtmp-27_notes2-2 -...

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