A with det a 0 10 01 false consider a with det a 0 00

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A = , with det( A ) = 0. 10 01
False. Consider A = , with det( A ) = 0. 00 10 False. Consider A = , with det( A ) = 0. 01 00 ,
17. –/1 pointsHoltLinAlg1 5.1.074. Determine if the statement is true or false, and justify your answer. If A is a diagonal matrix, then is also diagonal for all i and M ij True, by the theorem that says if A is a diagonal matrix, then M ij is also diagonal for all i j . j . and 100 010 001 10 01
Solution or Explanation False. Consider then is not diagonal. False. Consider A = , then M 31 = is not diagonal. 100 010 001 10 01 False. Consider A = , then M 31 = is not diagonal. 100 010 001 00 10 False. Consider A = , then M 11 = is not diagonal. 100 010 001 00 10 A = , 1 0 0 0 1 0 0 0 1 M 31 = 0 0 1 0
18. –/1 pointsHoltLinAlg1 5.1.075. Determine if the statement is true or false, and justify your answer. If the cofactors of an matrix A are all nonzero, then but 0. 1 1 1 1 11 10 ) = 0. A ) = 0. .
19. –/1 pointsHoltLinAlg1 5.1.076. Determine if the statement is true or false, and justify your answer. If A and B are matrices, then True, by the distributive property of determinants. so ). 10 00 0 1 .
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