Mathematics II2080.15 marksNumerical: linear independence of vectorsLinear independence
Are vectors v1, v2, and v3 linearly independent? Justify.
Are vectors $v_1$, $v_2$, and $v_3$ linearly independent? Justify.
$$v_1 = \begin{bmatrix} 1 \ 4 \ 0 \end{bmatrix}, \quad v_2 = \begin{bmatrix} 10 \ 2 \ 1 \end{bmatrix}, \quad v_3 = \begin{bmatrix} -5 \ 0 \ 6 \end{bmatrix}$$
[5]
$$v1 = \begin{bmatrix} 1 \ 4 \ 0 \end{bmatrix},\quad v2 = \begin{bmatrix} 10 \ 2 \ 1 \end{bmatrix},\quad v3 = \begin{bmatrix} -5 \ 0 \ 6 \end{bmatrix}$$ The vectors are linearly independent iff the only solution to $c1 v1 + c2 v2 + c3 v3 = 0$ is the trivial one. For 3 vectors in