Exam 5: Determinants

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Partition matrix A to evaluate Partition matrix A to evaluate      , where   , where Partition matrix A to evaluate      , where

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If A is a If A is a     matrix, and B is an     matrix, then      . matrix, and B is an If A is a     matrix, and B is an     matrix, then      . matrix, then If A is a     matrix, and B is an     matrix, then      . .

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For all For all     matrices A,      . matrices A, For all     matrices A,      . .

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Find all values of a such that the matrix A is not invertible. Find all values of a such that the matrix A is not invertible.

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   . .

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Evaluate Evaluate      ,      ,      , and     where   , Evaluate      ,      ,      , and     where   , Evaluate      ,      ,      , and     where   , and Evaluate      ,      ,      , and     where   where Evaluate      ,      ,      , and     where

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If applicable, use Cramer's Rule to find the unique solution of the given linear system. If Cramer's Rule is not applicable, explain why. If applicable, use Cramer's Rule to find the unique solution of the given linear system. If Cramer's Rule is not applicable, explain why.

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If A and B are square matrices, and If A and B are square matrices, and      , then either     or      . , then either If A and B are square matrices, and      , then either     or      . or If A and B are square matrices, and      , then either     or      . .

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