- Solve the linear system by using Gaussian elimination:
$$\begin{bmatrix}
2 & 0 & 1\\
1 & 1 & 0\\
1 & 0 & 1
\end{bmatrix}\begin{bmatrix}
x\\
y\\
z
\end{bmatrix} = \begin{bmatrix}
1\\
2\\
3
\end{bmatrix}$$
-
Find the inverse of the above matrix by using Gaussian elimination, write down the rank of the matrix and explain why you get & didn’t get solutions for question 1.
-
Solve the system without using Gaussian elimination:
$$\begin{bmatrix}
2 & 0 & 1\\
1 & 1 & 0\\
1 & 0 & 1
\end{bmatrix}\begin{bmatrix}
x\\
y\\
z
\end{bmatrix} = \begin{bmatrix}
2\\
3\\
4
\end{bmatrix}$$