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Given that A is a 3 by 3 matrix and the det(A) = 4. We created a new matrix B from A by switching the row 1 and row 2 (This is the first elementary row operation). What is the det(B)? O-4 04 O We cannot find with the information given O 8

Given that A is a 3 by 3 matrix and the det(A) = 4. We created a new matrix B from A by switching the row 1 and row 2 (This is the first elementary row operation). What is the det(B)? O-4 04 O We cannot find with the information given O 8

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Question:** Given that A is a 3 by 3 matrix and det(A) = 4. We created a new matrix B from A by switching row 1 and row 2 (This is the first elementary row operation). What is the det(B)? - ❍ -4 - ❍ 4 - ❍ We cannot find with the information given - ❍ 8 **Explanation:** When performing the first elementary row operation of switching two rows in a matrix, the determinant of the new matrix is the negative of the determinant of the original matrix. Therefore, for matrix B, det(B) = -det(A). Given that det(A) = 4, det(B) = -4. Thus, the correct answer is -4.
Transcribed Image Text:**Question:** Given that A is a 3 by 3 matrix and det(A) = 4. We created a new matrix B from A by switching row 1 and row 2 (This is the first elementary row operation). What is the det(B)? - ❍ -4 - ❍ 4 - ❍ We cannot find with the information given - ❍ 8 **Explanation:** When performing the first elementary row operation of switching two rows in a matrix, the determinant of the new matrix is the negative of the determinant of the original matrix. Therefore, for matrix B, det(B) = -det(A). Given that det(A) = 4, det(B) = -4. Thus, the correct answer is -4.
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