Question

Find:
Let \(A=[a_{ij}]\) be a \(2\times2\) matrix whose elements are given by \[ a_{ij}=\frac{(2i-j)^2}{3} \] Find the transpose matrix \(A'\).

• A. \(\begin{bmatrix} \frac{1}{3} & 3 \\ 0 & \frac{4}{3} \end{bmatrix}\)
• B. \(\begin{bmatrix} \frac{1}{3} & 0 \\ 3 & \frac{4}{3} \end{bmatrix}\)
• C. \(\begin{bmatrix} \frac{4}{3} & 3 \\ 1 & 0 \end{bmatrix}\)
• D. \(\begin{bmatrix} \frac{4}{3} & 0 1 & \frac{3}{3} \end{bmatrix}\)

Hint:

Be careful not to confuse the matrix \(A\) with its transpose \(A'\). Double-check the position swaps: the element at row 1, column 2 (\(a_{12}\)) shifts to row 2, column 1 (\(a_{21}\)) in the transposed matrix.

Answer 1

The Correct Option is A