Transpose Of A Matrix - SS3 Mathematics Lesson Note

The transpose of a matrix \(A\) written \(A^{T}\) is a matrix obtained by interchanging the rows and columns of \(A\). In general, if \(A\) is an \((m \times n)\) matrix, \(A^{T}\)is an \((n \times m)\) matrix.

Given a matrix \(A = \begin{bmatrix} 3 & 4 & 0 & - 2 \\ 0 & 6 & - 1 & 6 \\ \end{bmatrix}\), \(A^{T} = \begin{bmatrix} 0 & 3 \\ 6 & 4 \\ - 1 & 0 \\ 6 & - 2 \\ \end{bmatrix}\)