Use inverse matrices to solve the system of linear equations.

Question

Use inverse matrices to solve the system of linear equations. ​  ​

Quizplus · Accepted Answer

The coefficient matrix is invertible since its determinant is not zero. Using the formula $x = A^{-1}b$, we can find the solution as follows:

$$\begin{bmatrix}
2 & 3 & -1 \
3 & -4 & 2 \
-1 & 2 & 7
\end{bmatrix}^{-1}
\begin{bmatrix}
3 \ -2 \ 4
\end{bmatrix} = 
\begin{bmatrix}
-11/29 \ -2/29 \ 17/29
\end{bmatrix}$$

Therefore, $x_1 = -11/29$, $x_2 = -2/29$, and $x_3 = 17/29$.

Use Inverse Matrices to Solve the System of Linear Equations