## Use Cramer’s Rule to Solve a $2\times 2$ System of Linear Equations

## Problem 257

Use Cramer’s rule to solve the system of linear equations

\begin{align*}

3x_1-2x_2&=5\\

7x_1+4x_2&=-1.

\end{align*}

Read solution

Use Cramer’s rule to solve the system of linear equations

\begin{align*}

3x_1-2x_2&=5\\

7x_1+4x_2&=-1.

\end{align*}

Read solution

Consider the system of linear equations

\begin{align*}

x_1&= 2, \\

-2x_1 + x_2 &= 3, \\

5x_1-4x_2 +x_3 &= 2

\end{align*}

**(a)** Find the coefficient matrix and its inverse matrix.

**(b)** Using the inverse matrix, solve the system of linear equations.

(*The Ohio State University, Linear Algebra Exam*)