# Is this set a basis for $ℝ^{3\times3}$?

I have a set of three matrices and want to know whether or not they form a basis for $ℝ^{3\times3}$

Any help is appreciated

the matrices: \begin{bmatrix}1&0&0\\0&1&0\\0 &0&1\end{bmatrix}\begin{bmatrix}0&1&0\\0&0&1\\0 &0&0\end{bmatrix}\begin{bmatrix}0&0&1\\0&0&0\\0 &0&0\end{bmatrix}

I know I have to show they are linearly independent and span the vector space, but I really don't get how I should do that

• What is the dimension of $\mathbb{R}^{3\times 3}$? – Ofir Jan 9 '17 at 11:05
Denote $C_1,C_2$ and $C_3$ the $3 \times 3$ matrices from your question. Is it true that $$\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 1 & 0 & 0 \end{bmatrix} \in \text{span}(C_1,C_2,C_3)?$$