# Thread: Linearly Independent

1. ## Linearly Independent

I need help on the following problem:

The vectors v = $\begin{bmatrix} 0\\-4\\-8 \end{bmatrix}$, u = $\begin{bmatrix} -4\\8\\28+k \end{bmatrix}$, and w = $\begin{bmatrix} 2\\-4\\-14 \end{bmatrix}$ are linearly independent if and only if $k \neq ?$

2. Originally Posted by MagicS06
I need help on the following problem:

The vectors v = $\begin{bmatrix} 0\\-4\\-8 \end{bmatrix}$, u = $\begin{bmatrix} -4\\8\\28+k \end{bmatrix}$, and w = $\begin{bmatrix} 2\\-4\\-14 \end{bmatrix}$ are linearly independent if and only if $k \neq ?$
The vectors are independet if and only if the following matrix has rank=3, so find k that makes rank<3

$\left ( \begin{array}{ccc} 0& -4& 2\\-4& 8&-4\\-8&24+k&-14\end{array}\right )$

3. or compute the determinant.