Question

If P=\(\begin{bmatrix}-1&5\\8&3\end{bmatrix}\) and Q=\(\begin{bmatrix}4&2\\8&5\end{bmatrix}\). Find (2P+3Q’)’.

(a) \(\begin{bmatrix}10&22\\34&21\end{bmatrix}\)

(b) \(\begin{bmatrix}10&21\\34&22\end{bmatrix}\)

(c) \(\begin{bmatrix}10&34\\22&21\end{bmatrix}\)

(d) \(\begin{bmatrix}10&22\\21&34\end{bmatrix}\)

This question was posed to me in homework.

This key question is from Transpose of a Matrix in division Matrices of Mathematics – Class 12

Answer 1

Right option is (a) \(\begin{bmatrix}10&22\\34&21\end{bmatrix}\)

For explanation I would say: Given that, P=\(\begin{bmatrix}-1&5\\8&3\end{bmatrix}\) and Q=\(\begin{bmatrix}4&2\\8&5\end{bmatrix}\)

⇒Q’=\(\begin{bmatrix}4&8\\2&5\end{bmatrix}\)

⇒2P+3Q’=2\(\begin{bmatrix}-1&5\\8&3\end{bmatrix}\)+3\(\begin{bmatrix}4&8\\2&5\end{bmatrix}\)=\(\begin{bmatrix}-2+12&10+24\\16+6&6+15\end{bmatrix}\)=\(\begin{bmatrix}10&34\\22&21\end{bmatrix}\)

∴(2P+3Q’ )’=\(\begin{bmatrix}10&22\\34&21\end{bmatrix}\).