If A= [ rrr 1 & -2 & 1 2 & 1 & 3 ] and B= [ ll 2 & 1 3 & 2 1 & 1 … - Vidyadip

MCQ

If $A=\left[\begin{array}{rrr}1 & -2 & 1 \\ 2 & 1 & 3\end{array}\right]$ and $B=\left[\begin{array}{ll}2 & 1 \\ 3 & 2 \\ 1 & 1\end{array}\right]$, then $(A B)^T$ is equal to

A
$\left[\begin{array}{rr}-3 & -2 \\ 10 & 7\end{array}\right]$
✓
$\left[\begin{array}{rr}-3 & 10 \\ -2 & 7\end{array}\right]$
C
$\left[\begin{array}{ll}-3 & 7 \\ 10 & 2\end{array}\right]$
D
None of these

✓

Answer

Correct option: B.

$\left[\begin{array}{rr}-3 & 10 \\ -2 & 7\end{array}\right]$

(b) : $A B=\left[\begin{array}{rrr}1 & -2 & 1 \\ 2 & 1 & 3\end{array}\right]\left[\begin{array}{ll}2 & 1 \\ 3 & 2 \\ 1 & 1\end{array}\right]=\left[\begin{array}{rr}-3 & -2 \\ 10 & 7\end{array}\right]$
$
\Rightarrow \quad(A B)^T=\left[\begin{array}{rr}
-3 & 10 \\
-2 & 7
\end{array}\right]
$

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