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Linear Algebra

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Moderate

Counting Free Variables 2

LINALG-SXBY2I

In the system $A\vec{x}=\vec{b}$ where:

$$A=\begin{pmatrix} 0 & 0 &0 &1 &2 &-1\\\ 1 & 2 &0 &0 &1 &-1\\\ 1 &2 & 2 &0 &-1&1\end{pmatrix}$$

$$\vec{x}=\begin{pmatrix}x_1\\\ x_2\\\ x_3\\\ x_4\\\ x_5\\\ x_6\end{pmatrix}$$

$$\vec{b}=\begin{pmatrix} 2 \\\ 0 \\\ 2\end{pmatrix}$$

...the solution set has:

A

$5$ free variables and $1$ non-free variable.

B

$4$ free variables and $2$ non-free variables.

C

$3$ free variables and $3$ non-free variables.

D

$0$ free variables and $6$ non-free variables.