If A = \(\begin{bmatrix} -3 & 4\\ 0 & 1 \end{bmatrix}\) then A - A^T is equal to ?

Question

Question

Answer 1

Concept:

Transpose of a Matrix:

The new matrix obtained by interchanging the rows and columns of the original matrix is called as the transpose of the matrix.

It is denoted by A′ or A^T

Calculation:

Given:

A = \(\begin{bmatrix} -3 & 4\\ 0 & 1 \end{bmatrix}\)

Now find the transpose of a matrix A,

A^T = \(\begin{bmatrix} -3 & 0\\ 4 & 1 \end{bmatrix}\)

Now,

A - AT = \(\begin{bmatrix} -3 & 4\\ 0 & 1 \end{bmatrix}-\begin{bmatrix} -3 & 0\\ 4 & 1 \end{bmatrix}\)

\(= \begin{bmatrix} 0 &4 \\ -4&0 \end{bmatrix}\)