Answer
See answers below
Work Step by Step
a) $\begin{bmatrix}
3&-1 & 6\\
0& 2 & 3\\
3 & -5 & 0
\end{bmatrix} \approx^1
\begin{bmatrix}
1&-\frac{1}{3} &2\\
0& 2 & 3\\
1 & -\frac{5}{3} & 0
\end{bmatrix} \approx^2\begin{bmatrix}
1&-\frac{1}{3} &2\\
0& 2 & 3\\
0 & -\frac{4}{3} & -2
\end{bmatrix} \approx^3 \begin{bmatrix}
1&-\frac{1}{3} &2\\
0& 2 & 3\\
0 & 0 & 0
\end{bmatrix} \approx^4 \begin{bmatrix}
1&-\frac{1}{3} &2\\
0& 1 & \frac{3}{2}\\
0 &0 &0
\end{bmatrix}$
$1.M_1(\frac{1}{2}),M_3(\frac{1}{3})$
$2.A_{13}(-1)$
$3.A_{23}(\frac{2}{3})$
$4.M_2(\frac{1}{2})$
b) $rank(A)=2$
c) Since $rank(A)=1 \lt 3$, A is not invertible
