Math Help - What is the dimension of V ? Find a basis for V

1. What is the dimension of V ? Find a basis for V

Just question (c). And only the first couple of steps.

Any help is appreciated!

2. $\begin{bmatrix}
1 & 0\\
2 & 1\\
0 & 2\\
3 & 1
\end{bmatrix}
$
rref= $\begin{bmatrix}
1 & 0\\
0 & 1\\
0 & 0\\
0 & 0
\end{bmatrix}$

The row rank is 2.

$x_1=0$ and $x_2=0$.

The nullity is $\mathbf{0}$.

3. Originally Posted by dwsmith
$\begin{bmatrix}
1 & 0\\
2 & 1\\
0 & 2\\
3 & 1
\end{bmatrix}
$
rref= $\begin{bmatrix}
1 & 0\\
0 & 1\\
0 & 0\\
0 & 0
\end{bmatrix}$

The row rank is 2.

$x_1=0$ and $x_2=0$.

The nullity is $\mathbf{0}$.

What is the basis?

4. Nullity = Dim

The basis are the vectors that span the nullity.