Det a λ i 2 0 a 7 4 8 1 λ dne det a λ i 2 det λ det λ

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det(AλI2) = 0A=7481λ=$$DNEdet(AλI2) = detλ= det=λ26λ+2574811 00 17λ8λ1(6)24(1)(25) =64< 0.= 04
10.3/3 points |Previous AnswersHoltLinAlg1 5.1.050.Determine all real values ofλsuch thefor the given matrixA. (Enter your answers asa comma-separated list. If an answer does not exist, enter DNE.)=5.7λ
11.5/5 points |Previous AnswersHoltLinAlg1 5.1.053.For each given matrixA, first compute det(A). Then interchange two rows of your choosing and computethe determinant of the resulting matrixA'.(a)(b)Form a conjecture about the effect of row interchanges on determinants.Solution or ExplanationA=4 23 5det(A) =2626det(A') =-26-26A=1312030 11det(A) =11det(A') =-1-1Interchanging rows does not change the determinant.Interchanging rows halves the determinant.Interchanging rows has no consistent effect on the determinant.Interchanging rows doubles the determinant.Interchanging rows changes the sign of the determinant..
12.5/5 points |Previous AnswersHoltLinAlg1 5.1.057.For each given matrixA, first compute det(A). Then multiply a row of your choosing by 3 and computethe determinant of the resulting matrixA'.(a)(b)Form a conjecture about the effect on determinants of multiplying a row times a scalar.Solution or Explanation(a)(b)0 110 11.A=3 25 4det(A) =2222det(A') =6666A=1312030 11det(A) =11det(A') =33Multiplying a row bycdoes not change the determinant.Multiplying a row bycchanges the sign of the determinant.Multiplying a row bychas no consistent effect on the determinant.Multiplying a row bycmultiplies the determinant byc.Multiplying a row bycdivides the determinant byc.det=22; multiplying row 1 by 3, det=66.3 25 49 65 4det= 1; multiplying row 1 by 3, det= 3.131203393203

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Term
Fall
Professor
N/A
Tags
Math, Linear Algebra, Algebra, Characteristic polynomial, Invertible matrix, Triangular matrix, Det

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