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Use the cofactor expansion to compute the following determinant: 0-9-92 0 7-54 det = 0 -4 10 4 8 05-17

Use the cofactor expansion to compute the following determinant: 0-9-92 0 7-54 det = 0 -4 10 4 8 05-17

Intermediate Algebra
Intermediate Algebra
19th Edition
ISBN:9780998625720
Author:Lynn Marecek
Publisher:Lynn Marecek
Chapter4: Systems Of Linear Equations
Section4.5: Solve Systems Of Equations Using Matrices
Problem 4.78TI: Perform the indicated operations on the augmented matrix: (a) Interchange rows 1 and 2, (b) Multiply...
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Use the cofactor expansion to compute the following determinant: 0-9-92 0 7-54 det = 0 -4 10 4 8 0 5-17
Transcribed Image Text:Use the cofactor expansion to compute the following determinant: 0-9-92 0 7-54 det = 0 -4 10 4 8 0 5-17
Let A be a 2×2 matrix and suppose that det(A)=4. For each of the following row operations, determine the value of det(B), where B is the matrix obtained by applying that row operation to A. a) Add -5 times row 1 to row 2 b) Interchange rows 2 and 1 c) Multiply row 2 by -3 Resulting values for det(B): a) det(B) = 0 b) det(B) = 0 c) det(B) = 0 Comments: The correct answer for a) is: det(B)=4. Adding a multiple of a row to another row does not affect the value of the determinant. The correct answer for b) is: det(B)=-4. Interchanging two rows negates the value of the determinant. The correct answer for c) is: det(B)=-12. Multiplying a row by a scalar multiplies the value of the determinant by the same scalar.
Transcribed Image Text:Let A be a 2×2 matrix and suppose that det(A)=4. For each of the following row operations, determine the value of det(B), where B is the matrix obtained by applying that row operation to A. a) Add -5 times row 1 to row 2 b) Interchange rows 2 and 1 c) Multiply row 2 by -3 Resulting values for det(B): a) det(B) = 0 b) det(B) = 0 c) det(B) = 0 Comments: The correct answer for a) is: det(B)=4. Adding a multiple of a row to another row does not affect the value of the determinant. The correct answer for b) is: det(B)=-4. Interchanging two rows negates the value of the determinant. The correct answer for c) is: det(B)=-12. Multiplying a row by a scalar multiplies the value of the determinant by the same scalar.
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