Find a basis for the null space of the matrix
\[\begin{bmatrix} 0 & -5 & 10 & -4 \\ -5 & -4 & 3 & 3 \\ 0 & 1 & -2 & -2 \end{bmatrix}.\]Click for answer
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\[ \begin{bmatrix} 0 & -5 & 10 & -4 \\ -5 & -4 & 3 & 3 \\ 0 & 1 & -2 & -2 \end{bmatrix} \]Solution:
\begin{solution} Reduced Row Echelon Form: \[\begin{bmatrix} 1 & 0 & 1 & 0 \\ 0 & 1 & -2 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}\] Basis: \[\begin{bmatrix} -1 \\ 2 \\ 1 \\ 0 \end{bmatrix}, \qquad \] \end{solution}