Linear Algebra

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Moderate

Equivalent Matrix Representations

LINALG-J13OXR

Given the system:

$$\begin{align*}3x_1+2x_2-x_3 &= -1\\\ 2x_1-4x_2+2x_3&=2 \\\ -x_1+6x_2+3x_3 &= 7\end{align*}$$

...which matrix equations have the same solution set as this system?

Select ALL that apply.

A

$\begin{pmatrix} 3 & 2 & -1\\\ 2 &-4&2 \\\ -1 &6 &3\end{pmatrix}\begin{pmatrix}x_1\\\ x_2\\\ x_3\end{pmatrix}=\begin{pmatrix} -1 \\\ 7 \\\ 2\end{pmatrix}$

B

$\begin{pmatrix} 3 & 2 & -1\\\ -1 &6&3 \\\ 2 &4 &2\end{pmatrix}\begin{pmatrix}x_1\\\ x_2\\\ x_3\end{pmatrix}=\begin{pmatrix} -1 \\\ 7 \\\ 2\end{pmatrix}$

C

$\begin{pmatrix} 6 & 4 & -2\\\ 2 &-4&2 \\\ -1 &6 &3\end{pmatrix}\begin{pmatrix}x_1\\\ x_2\\\ x_3\end{pmatrix}=\begin{pmatrix} -2 \\\ 2 \\\ 7\end{pmatrix}$

D

$\begin{pmatrix} 3 & 2 & -1\\\ 2 &-4&2 \\\ -1 &6 &3\end{pmatrix}\begin{pmatrix}x_1\\\ x_3\\\ x_2\end{pmatrix}=\begin{pmatrix} -1 \\\ 7 \\\ 2\end{pmatrix}$

E

$\begin{pmatrix} 1 & 0 & 0\\\ 0 &1&0 \\\ 0 &0 &1\end{pmatrix}\begin{pmatrix}x_1\\\ x_2\\\ x_3\end{pmatrix}=\begin{pmatrix} 0 \\\ 1/3 \\\ 5/3\end{pmatrix}$