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Consider the vectors \(\mathbf{v} = \begin{pmatrix} 1\\3 \end{pmatrix}, \mathbf{w} = \begin{pmatrix} 3\\2 \end{pmatrix}\), and \(\mathbf{x} = \begin{pmatrix}1 \\ 0 \end{pmatrix}.\)

If the vectors v, w, and x are linearly independent, answer with 0. If they aren't, find coefficients a, b, and c, not all 0, such that \(a \begin{pmatrix} 1 \\ 3 \end{pmatrix} + b \begin{pmatrix} 3 \\ 2 \end{pmatrix} + c \begin{pmatrix} 1 \\ 0 \end{pmatrix} = \begin{pmatrix}0 \\ 0 \end{pmatrix}\)and answer with (a+b)/c.

 Oct 6, 2019
 #1
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3 2D vectors cannot be linearly independent.

 

By eye

a=2

b=-3

c=7

 

5/7

 Oct 7, 2019
edited by Rom  Oct 7, 2019

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