- #1

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## Homework Statement

Why does no 3 by 3 matrix have a nullspace that equals its column space?

## Homework Equations

NA

## The Attempt at a Solution

[tex]

A =

\begin{bmatrix}

0 & 0 & 1 \\

0 & 0 & 0 \\

0 & 0 & 0

\end{bmatrix}

\]

[/tex]

[tex]

C(A) =

\begin{bmatrix}

1 \\

0 \\

0

\end{bmatrix}

\]

[/tex]

Does not then N(A) = C(A)?

I think I am missing something here.

Thank you for your time.