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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
MCQ
If $A=\left[\begin{array}{r}1 \\ -4 \\ 3\end{array}\right]$ and $B=\left[\begin{array}{lll}-1 & 2 & 1\end{array}\right]$, then $(A B)^{\prime}$ is equal to
  • ✓
    $\left[\begin{array}{rrr}-1 & 4 & -3 \\ 2 & -8 & 6 \\ 1 & -4 & 3\end{array}\right]$
  • B
    $\left[\begin{array}{rrr}-1 & 2 & 1 \\ 4 & -8 & -4 \\ -3 & 6 & 3\end{array}\right]$
  • C
    $\left[\begin{array}{rrr}1 & 4 & -3 \\ 2 & -8 & 6 \\ 1 & 4 & 3\end{array}\right]$
  • D
    $\left[\begin{array}{rrr}-1 & 4 & -3 \\ 2 & 8 & 6 \\ 1 & -4 & 3\end{array}\right]$
✓

Answer

Correct option: A.
$\left[\begin{array}{rrr}-1 & 4 & -3 \\ 2 & -8 & 6 \\ 1 & -4 & 3\end{array}\right]$
(a) : $(A B)=\left[\begin{array}{c}1 \\ -4 \\ 3\end{array}\right]\left[\begin{array}{lll}-1 & 2 & 1\end{array}\right]=\left[\begin{array}{ccc}-1 & 2 & 1 \\ 4 & -8 & -4 \\ -3 & 6 & 3\end{array}\right]$
$
\therefore \quad(A B)^{\prime}=\left[\begin{array}{ccc}
-1 & 4 & -3 \\
2 & -8 & 6 \\
1 & -4 & 3
\end{array}\right]
$

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