Complete all problems below and upload to Gradescope by the due date. You must show all work
in order to receive credit. Correct answers with no work justifying the answer will get no credit.
(1) Consider the following system of linear equations:
$3x_1 - 2x_2 + 4x_3 + 8x_4 = 1$,
$7x_1 + 11x_2 + x_3 - x_4 = 0$,
$5x_1 + 6x_2 - 9x_3 + 6x_4 = 3$,
$x_1 + x_2 - x_3 + 12x_4 = 8$.
(i) Write the above system as $Ax = b$ where $A \in \mathbb{R}^{4x4}$, $b \in \mathbb{R}^4$ and $x$ is a vector of
variables.
(ii) Find the augmented matrix of the system. Call this matrix $M$.
(iii) Find the echelon form of $M$ using elementary row operations.
(iv) Find the reduced echelon form of $M$ using elementary row operations.
(v) Find the solution set of the above system.
