8. If \( A=\left[\begin{array}{ll}1 & 3 \\ 4 & 1\end{array}\right] \), then find \( \left|3 A^{\prime}\right| \).
1 Answers
Matrix A \(=\begin{bmatrix}1&3\\4&1\end{bmatrix}_{2\times2}\)
|3 A'| = 2
\(A'=\begin{bmatrix}1&4\\3&1\end{bmatrix}_{2\times2}\)
We know that
⇒ |K A| = (K)3 |A|
⇒ |3 A'| = 32 |A'|
\(A'=\begin{bmatrix}1&4\\3&1\end{bmatrix}\)
⇒ |A'| = 1 x 1 - 4 x 3
⇒ 1 - 12
= -11
⇒ |3 A'| = (32) |A'|
= 9 x |(A')|
= 9 x (-11)
|3 A'| = -99
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