Q15Multiple correct3 Marks7 Jul 2024

Let $Ax=b$ be a system of linear equations, where $A=\begin{bmatrix}1&0&0&-1\\0&0&1&5\\0&0&0&1\end{bmatrix}$, $x=\begin{bmatrix}x_1&x_2&x_3&x_4\end{bmatrix}^T$, and $b\in\mathbb{R}^3$. Which of the following statements are true?

A

$A$ is in row echelon form.

B

$x_2$ is an independent variable.

C

After reducing the system to reduced row echelon form, the value of $x_3$ is dependent on the value of $x_4$ in the solution vector.

D

When $b=\begin{bmatrix}1&-2&3\end{bmatrix}^T$, the system has infinitely many solutions.

E

The system has $2$ dependent and $2$ independent variables.