# A 5 2 3 4 det a no response 26 det a no response 78 a

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A=5 23 4det(A) =(No Response)26det(A') =(No Response)78A=1213020 11det(A) =(No Response)1det(A') =(No Response)3det=26; multiplying row 1 by 3, det=78.5 23 415 63 4det= 1; multiplying row 1 by 3, det= 3.1213020 113633020 11
13.–/1 pointsHoltLinAlg1 5.1.069.Determine if the statement is true or false, and justify your answer.Every matrixAhas a determinant.True, by the theorem that says all matrices have determinants.
False. Everynonsquarematrix has a determinant, but square matrices do not.A=1 3 12 1 7
14.–/1 pointsHoltLinAlg1 5.1.070.Determine if the statement is true or false, and justify your answer.IfAis anmatrix, then each cofactor ofAis anmatrix.True, since each cofactor is created by removing one column and one row fromAFalse. The cofactors are vectors, not matrices.n×n(n1)×(n1).
15.–/1 pointsHoltLinAlg1 5.1.071.Determine if the statement is true or false, and justify your answer.IfAis anmatrix with all positive entries, thenTrue, since ifA=, then det(A) =adbc, which is positive for alla,b,c,abcdabcdSolution or Explanationd> 0.d> 0.False. ConsiderA=, which has det(A) =1.2111False. ConsiderA=, which has det(A) =1.1211False. ConsiderA=, which has det(A) =1.1112A=,1 21 1det(A) =1.
16.–/1 pointsHoltLinAlg1 5.1.073.Determine if the statement is true or false, and justify your answer.IfAis an upper triangularmatrix, thenSolution or ExplanationTrue. IfAis an upper triangularn×nmatrix, then it is invertible with a nonzero determinant.True. IfAis an upper triangularn×nmatrix, then it is singular with a nonzero determinant.

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Math, Characteristic polynomial, Invertible matrix, Triangular matrix, Det
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