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If \( A=\left[\begin{array}{ll}1 & 3 \\ 4 & 2\end{array}\right], B=\left[\begin{array}{cc}2 & -1 \\ 1 & 2\end{array}\right] \) then \( \left|A B B^{\prime}\right|= \)
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2340 Upvotes
Verified Answer
The correct answer is:
\( -250 \)
(A)
\[
\begin{array}{l}
A=\left[\begin{array}{ll}
1 & 3 \\
4 & 2
\end{array}\right], B=\left[\begin{array}{cc}
2 & -1 \\
1 & 2
\end{array}\right] \\
B^{\prime}=\left[\begin{array}{cc}
2 & 1 \\
-1 & 2
\end{array}\right] \\
\left|A B B^{\prime}\right|=|A||B|\left|B^{\prime}\right| \\
=(2-12) \times(4+1) \times(4+1) \\
=-10 \times 5 \times 5=-250
\end{array}
\]
\[
\begin{array}{l}
A=\left[\begin{array}{ll}
1 & 3 \\
4 & 2
\end{array}\right], B=\left[\begin{array}{cc}
2 & -1 \\
1 & 2
\end{array}\right] \\
B^{\prime}=\left[\begin{array}{cc}
2 & 1 \\
-1 & 2
\end{array}\right] \\
\left|A B B^{\prime}\right|=|A||B|\left|B^{\prime}\right| \\
=(2-12) \times(4+1) \times(4+1) \\
=-10 \times 5 \times 5=-250
\end{array}
\]
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