## Determine Bases for Nullspaces $\calN(A)$ and $\calN(A^{T}A)$

## Problem 713

Determine bases for $\calN(A)$ and $\calN(A^{T}A)$ when

\[

A=

\begin{bmatrix}

1 & 2 & 1 \\

1 & 1 & 3 \\

0 & 0 & 0

\end{bmatrix}

.

\]
Then, determine the ranks and nullities of the matrices $A$ and $A^{\trans}A$.