Question

and B = 1 Find the matrix X such that 2x -B AX+I 8. Let A=100 1 1 3 3|1 2 12(b)2 1(d)2 32(c)

Answer 1

$\\2X-B = AX+I\\ \\(2+A)X = I+B\\ \\X = (2+A)^{-1}(I+B)\\ \\ = (\begin{bmatrix} 2 &0 \\ 0 &2 \end{bmatrix}+\begin{bmatrix} 1 &2 \\ 0 &0 \end{bmatrix})(\begin{bmatrix} 1 &0 \\ 0 & 1 \end{bmatrix}+\begin{bmatrix} 0 &-1 \\ 1 & 1 \end{bmatrix})\\ \\=\begin{bmatrix} 3 & 2\\ 0 &2 \end{bmatrix}^{-1}\begin{bmatrix} 1 &-1 \\ 1 &2 \end{bmatrix}\\ \\=\frac{1}{3}\begin{bmatrix} 1 &-1 \\ 0 &1.5 \end{bmatrix}\begin{bmatrix} 1 &-1 \\ 1 &2 \end{bmatrix}\\ \\=\frac{1}{3}\begin{bmatrix} 0 &-3 \\ 1.5&3 \end{bmatrix}$