Math 54 - Quiz 02 Ans, Spring 2006 (2)

# Math 54 - Quiz 02 Ans, Spring 2006 (2) - when it is row...

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Math 54, Quiz 2 Solutions Sections 202/203 GSI Carter For each of the following matrices, either compute its inverse or state that there is no inverse. In both matrices, a is a non-zero constant. 1. 1 a 0 0 0 1 - a 0 0 0 1 a 0 0 0 1 By row reduction, we get 1 a 0 0 1 0 0 0 0 1 - a 0 0 1 0 0 0 0 1 a 0 0 1 0 0 0 0 1 0 0 0 1 1 a 0 0 1 0 0 0 0 1 - a 0 0 1 0 0 0 0 1 0 0 0 1 - a 0 0 0 1 0 0 0 1 1 a 0 0 1 0 0 0 0 1 0 0 0 1 a - a 2 0 0 1 0 0 0 1 - a 0 0 0 1 0 0 0 1 1 0 0 0 1 - a - a 2 a 3 0 1 0 0 0 1 a - a 2 0 0 1 0 0 0 1 - a 0 0 0 1 0 0 0 1 So, the inverse is 1 - a - a 2 a 3 0 1 a - a 2 0 0 1 - a 0 0 0 1 2. a 4 3 0 2 1 - a - 2 - 2 The bottom row is the diﬀerence of the top two rows. Therefore, this matrix has a row of all zeroes
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Unformatted text preview: when it is row reduced, and it is not invertible. 1...
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