GATE 2017 CE (CE2) – Question 38

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors · 2 marks · Multiple choice

Given $$A=\begin{bmatrix}1&5\\6&2\end{bmatrix},\quad B=\begin{bmatrix}3&7\\8&4\end{bmatrix},$$ find $AB^T$.

$$\begin{bmatrix}38&28\\32&56\end{bmatrix}$$
$$\begin{bmatrix}3&40\\42&8\end{bmatrix}$$
$$\begin{bmatrix}43&27\\34&50\end{bmatrix}$$
$$\begin{bmatrix}38&32\\28&56\end{bmatrix}$$

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Correct answer: (A) $$\begin{bmatrix}38&28\\32&56\end{bmatrix}$$

Explanation

Transpose B, then multiply in the stated order: $$B^T=\begin{bmatrix}3&8\\7&4\end{bmatrix},\quad AB^T=\begin{bmatrix}3+35&8+20\\18+14&48+8\end{bmatrix}=\begin{bmatrix}38&28\\32&56\end{bmatrix}.$$ Answer A.