1. ## Linear Independence

Determine if the following vectors are linearly independent.

$\displaystyle \begin{bmatrix} 5 \\ 0 \\ 0 \end{bmatrix}$ , $\displaystyle \begin{bmatrix} 7 \\ 2 \\ -6 \end{bmatrix}$ , $\displaystyle \begin{bmatrix} 9 \\ 4 \\ -8 \end{bmatrix}$

When i row reduced the augmented matrix, i was getting no solution. Am I correct? And in a situation like that, how do you answer the question? What's the best way to phrase a response?? Or is there something that you do in situations of such?

Would be grateful for whatever help. Thanks a lot.

2. Originally Posted by Ife
Determine if the following vectors are linearly independent.

$\displaystyle \begin{bmatrix} 5 \\ 0 \\ 0 \end{bmatrix}$ , $\displaystyle \begin{bmatrix} 7 \\ 2 \\ -6 \end{bmatrix}$ , $\displaystyle \begin{bmatrix} 9 \\ 4 \\ -8 \end{bmatrix}$

When i row reduced the augmented matrix, i was getting no solution. Am I correct? And in a situation like that, how do you answer the question? What's the best way to phrase a response?? Or is there something that you do in situations of such?

Would be grateful for whatever help. Thanks a lot.
Did you try taking the determinant? If $\displaystyle \begin{vmatrix}5 & 7 & 9\\0 & 2 & 4\\ 0 & -6 & -8\end{vmatrix}=0$, its linearly dependent. Otherwise, its independent.

If you row reduce the augmented matrix, you shouldn't get no solution...