If [(1, 0, 0), (0, 1, 0), (0, 0, 1)][x, y, z] = [1, -1, 0], find x, y and z.

Question

If\(\begin{bmatrix} 1&0&0\\0&1&0\\0&0&1\end{bmatrix}\begin{bmatrix} x\\y\\z\end{bmatrix} \)= \(\begin{bmatrix} 1\\ -1\\0\end{bmatrix}, \) find x, y and z.

Answer 1

The given matrix equation is :

\(\begin{bmatrix} 1&0&0\\0&1&0\\0&0&1\end{bmatrix}\begin{bmatrix} x\\y\\z\end{bmatrix} \)= \(\begin{bmatrix} 1\\ -1\\0\end{bmatrix}\)

The first matrix is an identity matrix which is denoted by I .

As we know that any matrix when multiplied with the identity matrix will be the matrix itself. But here the order of I is 3 x 3 while the order of P is 3 x 1, so the order of the result matrix is 3 x 1.