Given P=pmatrix2&3&7\\4&1&5pmatrix and Q=pmatrix8&11&9\\12&6&13pmatrix,find PTQ.

$\begin{pmatrix}64&36&116\\46&39&107\\70&40&128\end{pmatrix}$

$\begin{pmatrix}112&113\\88&89\end{pmatrix}$

$\begin{pmatrix}112&88\\113&89\end{pmatrix}$

GATE 2024 AG – Question 36

Engineering Mathematics · Linear Algebra · 2 marks · Multiple choice

Given $P=\begin{pmatrix}2&3&7\\4&1&5\end{pmatrix}$ and $Q=\begin{pmatrix}8&11&9\\12&6&13\end{pmatrix}$,find $P^TQ$.

$\begin{pmatrix}64&36&116\\46&39&107\\70&40&128\end{pmatrix}$
$\begin{pmatrix}64&46&70\\36&39&40\\116&107&128\end{pmatrix}$
$\begin{pmatrix}112&113\\88&89\end{pmatrix}$
$\begin{pmatrix}112&88\\113&89\end{pmatrix}$

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Correct answer: (B) $\begin{pmatrix}64&46&70\\36&39&40\\116&107&128\end{pmatrix}$

Explanation

$P^T$ has rows(2,4),(3,1),(7,5). Dot these against Q’s columns(8,12),(11,6),(9,13). The resulting rows are(64,46,70),(36,39,40),(116,107,128),which is **B**. Dimensions are3×2 times2×3,giving3×3; the2×2 alternatives have incorrect dimensions.

GATE 2024 AG – Question 36

Explanation

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