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Linear Algebra

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Moderate

Solving Using Echelon Form

LINALG-4N3WZJ

Suppose that the linear system $A\mathbf{x}=\mathbf{b}$ has augmented matrix $M$ and the reduced row echelon form of $M$ is:

$$\operatorname{rref}(M) = \left[ \begin{matrix} 1 & 0 & 2 & 3 & 0 \\\ 0 & 1 & -1 & 1 & 0 \\\ 0 & 0 & 0 & 0 & 0 \end{matrix} \right]$$

Which of the following is a parametric description of the solution set?

A

$\{ (-2s-3t, s-t, s, t) : s,t \text{ free } \}$

B

$\{(2s-s, 3t+t, s, t): s,t \text{ free } \}$

C

$\{ (s,t, 2s -t, 3s +t) : s,t \text{ free } \}$

D

$\{ (-2s-3t, s-t, s+2t, 3s+t) : s,t \text{ free } \}$

E

The system is inconsistent/has no solutions