Linear Algebra Quiz
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SYSTEMS OF LINEAR EQUATIONS & MATRICES
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Consider the augmented matrix [12−13∣4001−2∣10000∣0]\begin{bmatrix} 1 & 2 & -1 & 3 & | & 4 \\ 0 & 0 & 1 & -2 & | & 1 \\ 0 & 0 & 0 & 0 & | & 0 \end{bmatrix} in reduced row echelon form. If the general solution is written as x=xp+sv1+tv2\mathbf{x} = \mathbf{x}_p + s\mathbf{v}_1 + t\mathbf{v}_2 where ss and tt are parameters, which of the following correctly identifies the relationship between the free variables and parameters?
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