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If A is a 2x2 matrix such that det(A) = 21, then what is det(5A)? Your Answer: Answer

If A is a 2x2 matrix such that det(A) = 21, then what is det(5A)? Your Answer: Answer

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: A Question** If \( A \) is a 2x2 matrix such that \(\text{det}(A) = 21\), then what is \(\text{det}(5A)\)? **Your Answer:** [Input Box] **Answer:** To solve this, recall that for any scalar \( c \) multiplied by an \( n \times n \) matrix \( A \), the determinant is given by \(\text{det}(cA) = c^n \times \text{det}(A)\). In this case, since \( A \) is a 2x2 matrix, \( n = 2 \), and \( c = 5 \). Therefore, \(\text{det}(5A) = 5^2 \times \text{det}(A) = 25 \times 21\).
Transcribed Image Text:**Matrix Determinants: A Question** If \( A \) is a 2x2 matrix such that \(\text{det}(A) = 21\), then what is \(\text{det}(5A)\)? **Your Answer:** [Input Box] **Answer:** To solve this, recall that for any scalar \( c \) multiplied by an \( n \times n \) matrix \( A \), the determinant is given by \(\text{det}(cA) = c^n \times \text{det}(A)\). In this case, since \( A \) is a 2x2 matrix, \( n = 2 \), and \( c = 5 \). Therefore, \(\text{det}(5A) = 5^2 \times \text{det}(A) = 25 \times 21\).
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