# Math Help - Null Space of a Matrix

1. ## Null Space of a Matrix

Hello everyone.

The matrix is

1 1 -1 2
2 2 -3 1
-1 -1 0 5

I calculated the null space of the matrix as

$Span((-1,1,0,0)^T,(-5,0,-3,1)^T)$

$(-1,1,0,0)^T, Span(-5,0,-3,1)^T$

Why can't I express the first as part of the linear combination (i.e. as part of the span)?

2. Originally Posted by Lord Darkin
Hello everyone.

The matrix is

1 1 -1 2
2 2 -3 1
-1 -1 0 5

I calculated the null space of the matrix as

$Span((-1,1,0,0)^T,(-5,0,-3,1)^T)$

$(-1,1,0,0)^T, Span(-5,0,-3,1)^T$
$\begin{bmatrix}1 & 1 & -1 & 2 \\ 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 6\end{bmatrix}$