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review_true_false - Solutions to practice problems for Test...

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Solutions to practice problems for Test 4 1. Label the following statements as true or false . false (a) For any scalar k and square matrix A , det( kA )= k det( A ). true (b) For any n × n matrices, A and B , (det A )(det B )=det( AB ). true (c) For any n × n matrices, A and B , det( AB ) =det( BA ). false (e) The dimension of the eigenspace corresponding to an eigenvalue λ is equal to the multiplicity of λ as an eigenvalue. true (d) Asquarematrix A isnotinvertibleifandonlyif0isaneigenvalue of A . false (f) If A is diagonalizable, then A is invertible. false (g) If A is invertible, then A is diagonalizable. false (h) For any scalar c , bardbl cvectorv bardbl = c bardbl vectorv bardbl
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