Find the coordinator [X]B $$b_1 = \begin{bmatrix} 1 \\ -1 \\ -3 \end{bmatrix}, b_2 = \begin{bmatrix} -3 \\ 4 \\ 9 \end{bmatrix}, b_3 = \begin{bmatrix} 2 \\ -2 \\ 4 \end{bmatrix}, x = \begin{bmatrix} 8 \\ -9 \\ 6 \end{bmatrix}$$
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This means we want to find scalars $c_1, c_2, c_3$ such that $x = c_1b_1 + c_2b_2 + c_3b_3$. This can be written as a system of linear equations: $$c_1 \begin{bmatrix} 1 \\ -1 \\ -3 \end{bmatrix} + c_2 \begin{bmatrix} -3 \\ 4 \\ 9 \end{bmatrix} + c_3 Show more…
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