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2. Suppose A and B are 3 x 3 with det(4) = 3 and det(B) = -1. Compute the following. q (a) det(4¹) (b) det(-24²) (c) det(AB²) (d) det(34²B)

2. Suppose A and B are 3 x 3 with det(4) = 3 and det(B) = -1. Compute the following. q (a) det(4¹) (b) det(-24²) (c) det(AB²) (d) det(34²B)

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Matrix Determinants Problem** In this exercise, we are given two 3x3 matrices, \( A \) and \( B \), with the determinants \(\text{det}(A) = 3\) and \(\text{det}(B) = -1\). Your task is to compute the determinants of the following expressions: (a) \(\text{det}(A^4)\) (b) \(\text{det}(-2A^2)\) (c) \(\text{det}(AB^2)\) (d) \(\text{det}(3A^2B)\) Use the properties of determinants to solve each part. Remember: - \(\text{det}(A^n) = (\text{det}(A))^n\) - The determinant of a scalar multiple \( kA \) of a matrix \( A \) is \( k^n \cdot \text{det}(A) \) for an \( n \times n \) matrix. - \(\text{det}(AB) = \text{det}(A) \cdot \text{det}(B)\).
Transcribed Image Text:**Matrix Determinants Problem** In this exercise, we are given two 3x3 matrices, \( A \) and \( B \), with the determinants \(\text{det}(A) = 3\) and \(\text{det}(B) = -1\). Your task is to compute the determinants of the following expressions: (a) \(\text{det}(A^4)\) (b) \(\text{det}(-2A^2)\) (c) \(\text{det}(AB^2)\) (d) \(\text{det}(3A^2B)\) Use the properties of determinants to solve each part. Remember: - \(\text{det}(A^n) = (\text{det}(A))^n\) - The determinant of a scalar multiple \( kA \) of a matrix \( A \) is \( k^n \cdot \text{det}(A) \) for an \( n \times n \) matrix. - \(\text{det}(AB) = \text{det}(A) \cdot \text{det}(B)\).
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