Q1: Which of the following equations with unknowns $x_1$ and $x_2$ is linear?

A1: $x_1 - \sqrt{2} , x_2 = 4^3$

A2: $x_1 - \sqrt{2 x_2 } = 4^3$

A3: $x_1^2 - \sqrt{2 x_2 } = 4^3 $

A4: $ x_1^2 - 2 x_2 \cdot x_1 = 4 $

Q2: Consider the system of linear equations given by $$ x_1 + 2x_2 = 5 $$ $$ x_1 + x_2 = 3 $$ What is a solution for this system?

A1: $x_1 = 1$, $x_2 = 2$

A2: $x_1 = 1$, $x_2 = -2$

A3: $x_1 = 3$, $x_2 = 5$

A4: $x_1 = 2$, $x_2 = 3$

Q3: Which of the following equations represents a system of linear equations with $3$ equations and $2$ unknowns?

A1: $$ \begin{pmatrix} 1 & 3 \ 4 & 2 \ 0 & -4 \end{pmatrix} \begin{pmatrix} x_1 \ x_2 \end{pmatrix} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} $$

A2: $$ \begin{pmatrix} 1 & 3 \ 4 & 2 \end{pmatrix} \begin{pmatrix} x_1 \ x_2 \end{pmatrix} = \begin{pmatrix} 1 \ 2 \end{pmatrix} $$

A3: $$ \begin{pmatrix} 1 & 3 \ 4 & 2 \end{pmatrix} \begin{pmatrix} x_1 \ x_2 \ x_3 \end{pmatrix} = \begin{pmatrix} 1 \ 2 \end{pmatrix} $$

A4: $$ \begin{pmatrix} 1 & 3 & 2 \ 4 & 2 & 1 \end{pmatrix} \begin{pmatrix} x_1 \ x_2 \ x_3 \end{pmatrix} = \begin{pmatrix} 1 \ 2 \end{pmatrix} $$