## Algebra and Trigonometry 10th Edition

X =$\begin{bmatrix} 2 & -5 & 5\\ -5 & 0 & -6\\ \end{bmatrix}$
4B = -2X - 2A 2X = -2A - 4B X = $\frac{1}{2}$(-2A - 4B) First multiply matrix A by the scalar multiple -2: $\begin{bmatrix} -2(-2) & 1(-2) & 3(-2)\\ -1(-2) & 0(-2) & 4(-2)\\ \end{bmatrix}$ = $\begin{bmatrix} 4 & -2 & -6\\ 2 & 0 & -8\\ \end{bmatrix}$ Then multiply matrix B by the scalar multiple -4: $\begin{bmatrix} 0(-4) & 2(-4) & -4(-4)\\ 3(-4) & 0(-4) & 1(-4)\\ \end{bmatrix}$ = $\begin{bmatrix} 0 & -8 & 16\\ -12 & 0 & -4\\ \end{bmatrix}$ Then perform -2A + -4B to get matrix Y: Y = $\begin{bmatrix} 4+0 & -2-8 & -6+16\\ 2-12 & 0+0 & -8-4\\ \end{bmatrix}$ = $\begin{bmatrix} 4 & -10 & 10\\ -10 & 0 & -12\\ \end{bmatrix}$ Then multiply Y by the scalar $\frac{1}{2}$ to get X: X = $\begin{bmatrix} 4(\frac{1}{2}) & -10(\frac{1}{2}) & 10(\frac{1}{2})\\ -10(\frac{1}{2}) & 0(\frac{1}{2}) & -12(\frac{1}{2})\\ \end{bmatrix}$ = $\begin{bmatrix} 2 & -5 & 5\\ -5 & 0 & -6\\ \end{bmatrix}$