nullity and column space

[iNagib]

Hey fellas could use a hand on a linear question that has been bugging me.

 

Give an example of a 4 x 4 matrix such that col A = nul A

 

Appreciate any help!

Thanks,

ib

[Dave]

I thought about this a bit, but it's clear that the column-space and null-space must be intersection-free. So I presume that you mean rank(A) = nullity(A), in which case the answer is pretty straight-forward; just choose a matrix like

 

[math]\begin{pmatrix}

1 & 0 & 0 & 0\\

0 & 1 & 0 & 0\\

0 & 0 & 0 & 0\\

0 & 0 & 0 & 0

\end{pmatrix}[/math]