A First Course in Linear Algebra · Problem SS.C43

Vectors — Robert Beezer

Mathematics — Linear Algebra · spanning-sets

Problem

Suppose R={[2−1340],[1122−1],[3−103−2]}R = \left\{ \begin{bmatrix} 2 \\ -1 \\ 3 \\ 4 \\ 0 \end{bmatrix}, \begin{bmatrix} 1 \\ 1 \\ 2 \\ 2 \\ -1 \end{bmatrix}, \begin{bmatrix} 3 \\ -1 \\ 0 \\ 3 \\ -2 \end{bmatrix} \right\}. Is z=[11531]\mathbf{z} = \begin{bmatrix} 1 \\ 1 \\ 5 \\ 3 \\ 1 \end{bmatrix} in ⟨R⟩\langle R \rangle?

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