P+Q=pmatrix3&1\\2&12pmatrix and P-Q=pmatrix-1&-7\\8&2pmatrix. Find Q.

$\begin{pmatrix}1&-3\\5&7\end{pmatrix}$

$\begin{pmatrix}2&-3\\4&5\end{pmatrix}$

$\begin{pmatrix}1&0\\0&1\end{pmatrix}$

GATE 2021 ES – Question 36

Mathematics Foundation · Linear Algebra · 2 marks · Multiple choice

$P+Q=\begin{pmatrix}3&1\\2&12\end{pmatrix}$ and $P-Q=\begin{pmatrix}-1&-7\\8&2\end{pmatrix}$. Find Q.

$\begin{pmatrix}2&4\\-3&5\end{pmatrix}$
$\begin{pmatrix}1&-3\\5&7\end{pmatrix}$
$\begin{pmatrix}2&-3\\4&5\end{pmatrix}$
$\begin{pmatrix}1&0\\0&1\end{pmatrix}$

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Correct answer: (A) $\begin{pmatrix}2&4\\-3&5\end{pmatrix}$

Explanation

Subtract the second equation from the first:2Q=(4,8;−6,10). Dividing every entry by 2 gives $Q=\begin{pmatrix}2&4\\-3&5\end{pmatrix}$,**A**. Adding the equations would instead determine P.

GATE 2021 ES – Question 36

Explanation

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