Toronto Math Forum
MAT2442019F => MAT244Lectures & Home Assignments => Chapter 7 => Topic started by: aremorov on November 10, 2019, 09:17:34 PM

This is related to section 7.3 (specifically question 13 in the module).
How would we show whether the vectors $\vec{v_1}, \vec{v_2}, \vec{v_3}$ are linearly independent, where:
$\vec{v_1} = \begin{bmatrix}e^t \\ e^{3t}\end{bmatrix}$,
$\vec{v_2} = \begin{bmatrix}e^{4t} \\ e^{5t}\end{bmatrix}$
$\vec{v_3} = \begin{bmatrix}e^{2t} \\ e^{7t}\end{bmatrix}$
Taking the determinant $\vec{v_1} \quad \vec{v_2} \quad \vec{v_3}$ doesn't make sense...

Those are not just vectors, but vectorvalued functions and you need to check that for constant coefficients their linear combination is identically $0$ if and only if these coefficients are $0$.
Try first to look at components of this vectorfunction.