Solving Systems Using Matrix Inverses Practice Test

Solve the system using the inverse of the coefficient matrix.

\begin{align*}

2x+y&=5\

3x+4y&=7

\end{align*}

Let $A=\begin{bmatrix}2&1\3&4\end{bmatrix}$, $X=\begin{bmatrix}x\y\end{bmatrix}$, and $B=\begin{bmatrix}5\7\end{bmatrix}$. Compute $A^{-1}$ (by hand) and then $X=A^{-1}B$. What is $(x,y)$?

A system is written in matrix form $AX=B$. Determine whether $A$ is invertible (has an inverse). If it is invertible, you may solve using $X=A^{-1}B$.

$$A=\begin{bmatrix}1&2&3\2&4&6\1&0&1\end{bmatrix},\quad X=\begin{bmatrix}x\y\z\end{bmatrix},\quad B=\begin{bmatrix}1\2\3\end{bmatrix}.$$

Which statement is true?