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## Main Question or Discussion Point

So the matrix is just a row vector

[tex]\begin{bmatrix}3 & 4 & 0\end{bmatrix}[/tex]

My problem, is that I get the nullspace as having to 2 dimensions, and the row space as having 2 dimenions, but that adds up to 4 dimensions, when it should add up to three. What simple thing am I missing?

Null space base vectors

[tex]\begin{bmatrix}-4\\3\\0\end{bmatrix},\begin{bmatrix}0\\0\\1\end{bmatrix}[/tex]

Row space base vectors

[tex]\begin{bmatrix}1\\0\\0\end{bmatrix},\begin{bmatrix}0\\1\\0\end{bmatrix}[/tex]

[tex]\begin{bmatrix}3 & 4 & 0\end{bmatrix}[/tex]

My problem, is that I get the nullspace as having to 2 dimensions, and the row space as having 2 dimenions, but that adds up to 4 dimensions, when it should add up to three. What simple thing am I missing?

Null space base vectors

[tex]\begin{bmatrix}-4\\3\\0\end{bmatrix},\begin{bmatrix}0\\0\\1\end{bmatrix}[/tex]

Row space base vectors

[tex]\begin{bmatrix}1\\0\\0\end{bmatrix},\begin{bmatrix}0\\1\\0\end{bmatrix}[/tex]