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Math225Quiz5 - A = 2 1-2-1-1 2 1-1 2 This matrix is not...

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Math 225, Fall 2010 Quiz 5 Given an n × n matrix A , we know that the following are equivalent: a) A is invertible (i.e. it has an inverse matrix A - 1 ), b) Whenever A v = 0 , we know that v = 0 . c) For any b , there exists v such that A v = b . Now consider the specific matrix
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Unformatted text preview: A = 2 1-2-1-1 2 1-1 2 This matrix is not invertible. So b) and c) both fail to hold. Give explicit numerical examples to show that both b) and c) fail to hold....
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