1

**Chapter 7 / Finding linear independence**

« **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...

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...