Question

# Use the given inverse of the coefficient matrix to solve the following system 5x_1+3x_2=6 -6x_1-3x_2=-2 A^{-1}=\begin{bmatrix}-1 & -1 \\2 & \frac{5}{3} \end{bmatrix}

Matrix transformations
Use the given inverse of the coefficient matrix to solve the following system
$$5x_1+3x_2=6$$
$$-6x_1-3x_2=-2$$
$$A^{-1}=\begin{bmatrix}-1 & -1 \\2 & \frac{5}{3} \end{bmatrix}$$

## Expert Answers (2)

2021-05-20
2021-09-09

$$Ax=B$$

$$x=A^{-1}B$$

$$\left(\begin{array}{c}x_1\\ x_2\end{array}\right)=\left(\begin{array}{c}-1&-1\\ 2&\frac{5}{3}\end{array}\right)\left(\begin{array}{c}6\\-2\end{array}\right)$$

$$=\left(\begin{array}{c}(-1)(6)+(-1)(-2)\\(2)(6)+(\frac{5}{3})(-2)\end{array}\right)$$

$$\left(\begin{array}{c}x_1\\x_2\end{array}\right)=\left(\begin{array}{c}-6+2\\ 12-\frac{10}{3}\end{array}\right)$$

$$=\left(\begin{array}{c}-4\\\frac{26}{3}\end{array}\right)$$

So, $$x_1=-4\ x_2=\frac{26}{3}$$