# Det a λ i 2 0 a 8 4 7 1 λ no response det a λ i 2 det

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det(AλI2) = 0A=8471λ=(No Response)det(AλI2) = detλ= det=λ27λ+2084711 00 18λ7λ1(7)24(1)(20) =31< 0.= 04
10.–/3 pointsHoltLinAlg1 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.)λλ=4.7λ
11.–/5 pointsHoltLinAlg1 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.Interchanging rows halves the determinant.Interchanging rows doubles the determinant.Interchanging rows changes the sign of the determinant.Interchanging rows does not change the determinant.Interchanging rows has no consistent effect on the determinant.Solution or ExplanationA=3 45 2det(A) =(No Response)26det(A') =(No Response)-26A=1312030 11det(A) =(No Response)1det(A') =(No Response)-1det=26; interchanging rows, det=26.3 45 25 23 4
12.–/5 pointsHoltLinAlg1 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.Multiplying a row bycchanges the sign of the determinant.Multiplying a row bycdivides the determinant byc.Multiplying a row bychas no consistent effect on the determinant.Multiplying a row bycmultiplies the determinant byc.Multiplying a row bycdoes not change the determinant.Solution or Explanation.

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