Question

Find the transpose of the matrix A=\(\begin{bmatrix}-1&2&\sqrt{3}\\-4&5&\sqrt{6}\\-7&8&-9\end{bmatrix}\)

(a) \(\begin{bmatrix}1&-2&-\sqrt{3}\\4&-5&-\sqrt{6}\\7&-8&9\end{bmatrix}\)

(b) \(\begin{bmatrix}-1&-4&-7\\2&5&8\\\sqrt{3}&\sqrt{6}&-9\end{bmatrix}\)

(c) \(\begin{bmatrix}1&4&7\\-2&-5&-8\\-\sqrt{3}&-\sqrt{6}&9\end{bmatrix}\)

(d) \(\begin{bmatrix}1&4&7\\-2&5&2\\1&8&9\end{bmatrix}\)

I had been asked this question in my homework.

The above asked question is from Transpose of a Matrix topic in portion Matrices of Mathematics – Class 12

Answer 1

The correct choice is (b) \(\begin{bmatrix}-1&-4&-7\\2&5&8\\\sqrt{3}&\sqrt{6}&-9\end{bmatrix}\)

Easy explanation: To find the transpose of the matrix of the given matrix, interchange the rows with columns and columns with rows.

Hence, we get A’=\(\begin{bmatrix}-1&-4&-7\\2&5&8\\\sqrt{3}&\sqrt{6}&-9\end{bmatrix}\)