I need to know find all values of the parameter $t$, such that vectors $v, u, w$ span $\Bbb{R}^3$
$u= (1,1,1)$ $v=(1,5t,1)$ $w= (1,1, 25t^2)$
b) for which parameter $t$ is the set linearly independent?
c) for which parameter $t$ is the set dependent
I reached $$\begin{pmatrix}1&1&1&0\\0&5t-1&0&0\\0&0&25t^2&0\end{pmatrix}$$ and I am not sure if $t\neq \pm \frac15$ is a solution to the question regarding span and independence.. and if they are dependent in $ t= \pm \frac15$.