Solving Systems Using Matrix Inverses Practice Test

Use technology to solve the system by computing $X=A^{-1}B$.

$$

\begin{cases}

3x+y+z=9\

x+4y+z=9\

x+y+5z=17

\end{cases}

$$

In matrix form, $AX=B$ with

$$

A=\begin{bmatrix}3&1&1\1&4&1\1&1&5\end{bmatrix},\quad B=\begin{bmatrix}9\9\17\end{bmatrix}.

$$

What is $(x,y,z)$?

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?