1.

Which of the following set is basis for the subspace \(W = \left\{ \begin{bmatrix} x & y \\\ 0 & t \end{bmatrix}: x + 2y + t = 0, y + t = 0 \right\}\)

A. \( \left\{ \begin{bmatrix} -1 & 1 \\\ 2 & -1 \end{bmatrix} \right\}\)
B. \( \left\{ \begin{bmatrix} 1 & -1 \\\ 0 & 1 \end{bmatrix} \right\}\)
C. \( \left\{ \begin{bmatrix} 1 & 0 \\\ 0 & 0 \end{bmatrix} \begin{bmatrix} 0 & 1 \\\ 0 & 0 \end{bmatrix} \begin{bmatrix} 0 & 0 \\\ 0 & 1 \end{bmatrix} \right\}\)
D. \( \left \{\begin{bmatrix} 2 & 1 \\\ 0 & -1 \end{bmatrix} \begin{bmatrix} 1 & -1 \\\ 0 & 1 \end{bmatrix}\right \}\)
Answer» C. \( \left\{ \begin{bmatrix} 1 & 0 \\\ 0 & 0 \end{bmatrix} \begin{bmatrix} 0 & 1 \\\ 0 & 0 \end{bmatrix} \begin{bmatrix} 0 & 0 \\\ 0 & 1 \end{bmatrix} \right\}\)


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