Answer
See answer below
Work Step by Step
We are given $A=\begin{bmatrix}
1 & 1 & -1\\
0 & 1 & 7\\
0 & 0 & 1
\end{bmatrix}$
We notice that there is no free variable here. Hence:
$nullspace(A) = 0$
In this problem, according to the Rank-Nullity Theorem we have $n=3$. Further we see that $rank(A) = 3$. Hence:
$$rank(A)+nullity(A)=3+0=3=n$$
Hence the Rank-Nullity Theorem is verified.
