# Previous answers holtlinalg1 51069 determine if the

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13.1/1 points |Previous AnswersHoltLinAlg1 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. Everysquarematrix has a determinant, but nonsquare matrices do not.False. Everynonsquarematrix has a determinant, but square matrices do not.
14.1/1 points |Previous AnswersHoltLinAlg1 5.1.070.Determine if the statement is true or false, and justify your answer.IfAis anmatrix, then each cofactor ofAis anmatrix.n×n(n1)×(n1)True, since each cofactor is created by removing one column and one row fromA.False. The cofactors are vectors, not matrices.False. The cofactors are (n+ 1)×(n+ 1) matrices.
15.1/1 points |Previous AnswersHoltLinAlg1 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) =ad+bc, which is positive for alla,b,0.abcdTrue, since ifA=, then det(A) =adbc, which is positive for alla,b,c0.abcd1112c,d>,d>1.False. ConsiderA=, which has det(A) =1.1211False. ConsiderA=, which has det(A) =111.21,
16.1/1 points |Previous AnswersHoltLinAlg1 5.1.073.Determine if the statement is true or false, and justify your answer.IfAis an upper triangularmatrix, thenTrue. IfAis an upper triangularn×nmatrix, then it is singular with a nonzero determinant.True. IfAis an upper triangularn×nmatrix, then it is invertible with a nonzerodeterminant.False. ConsiderA=, with det(A) = 0.0100,
17.1/1 points |Previous AnswersHoltLinAlg1 5.1.074.Determine if the statement is true or false, and justify your answer.IfAis a diagonal matrix, thenis also diagonal for alliandMijTrue, by the theorem that says ifAis a diagonal matrix, thenMijis also diagonal for allandjj.i.1000100010010
False. ConsiderA=, thenM31=is not diagonal.1000100011001False. ConsiderA=, thenM31=is not diagonal.1000100010010False. ConsiderA=, thenM11=is not diagonal.1000100011001,

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