Question

Solve this system of equations using a matrix inverse, x+y=10 2x-z=9 y-3z=-5

Answer 1

Explanation:

Answer 2

Your system of equations is

`\left[ \begin{array}{ccc}1&1&0\\2&0&-1\\0&1&-3\end{array}\right]\cdot \left[ \begin{array}{c}x\\y\\z\end{array} \right] = \left[ \begin{array}{c}10\\9\\-5\end{array} \right]`

Then the solution is

`\left[ \begin{array}{c}x\\y\\z\end{array} \right] = \left[ \begin{array}{ccc}1&1&0\\2&0&-1\\0&1&-3\end{array}\right]^(-1)\cdot \left[ \begin{array}{c}10\\9\\-5\end{array} \right]`
Your graphing calculator or any of several web sites can compute the inverse matrix for you.

`\left[ \begin{array}{c}x\\y\\z\end{array} \right] = (1)/(7)\cdot \left[ \begin{array}{ccc}1&3&-1\\6&-3&1\\2&-1&-2\end{array}\right]\cdot \left[ \begin{array}{c}10\\9\\-5\end{array} \right] = \left[ \begin{array}{c}6\\4\\3\end{array} \right]`

The solution is (x, y, z) = (6, 4, 3).