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t Given that A =| u and det(A) = -5, evaluate the following: a. det(A) = b. det(AT) = С. det(3A) =

t Given that A =| u and det(A) = -5, evaluate the following: a. det(A) = b. det(AT) = С. det(3A) =

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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Given that \( A = \begin{bmatrix} r & s & t \\ u & v & w \\ x & y & z \end{bmatrix} \) and \(\det(A) = -5\), evaluate the following: a. \(\det(A^3) =\) b. \(\det(A^T) =\) c. \(\det(3A) =\) d. \(\det(A^{-1}) =\) e. \(\begin{vmatrix} 3x & 3y & 3z \\ u + r & v + s & w + t \\ r & s & t \end{vmatrix} =\)
Transcribed Image Text:Given that \( A = \begin{bmatrix} r & s & t \\ u & v & w \\ x & y & z \end{bmatrix} \) and \(\det(A) = -5\), evaluate the following: a. \(\det(A^3) =\) b. \(\det(A^T) =\) c. \(\det(3A) =\) d. \(\det(A^{-1}) =\) e. \(\begin{vmatrix} 3x & 3y & 3z \\ u + r & v + s & w + t \\ r & s & t \end{vmatrix} =\)
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