(Solved): Give an example of a matrix \( A \) and a vector \( b \) such that the solution set of \( A x=b \) ...

Give an example of a matrix \( A \) and a vector \( b \) such that the solution set of \( A x=b \) as a line in \( \mathrm{R}^{3} \) that does net contain the origin Suppose that a parametrization for the solution set to the equation \( A x=b \) is \[ \left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{c} -9 \\ -4 \\ 3 \end{array}\right]+x_{2}\left[\begin{array}{c} -7 \\ 4 \\ -6 \end{array}\right]+x_{3}\left[\begin{array}{c} 1 \\ 0 \\ -2 \end{array}\right] \] where \( z_{2} \) and \( x_{3} \) are free. Write a parametrization for the solution set to the equation \( A x=0 \) using the information above. Use \( x 3 \) and \( x 2 \) for the free variablos in necassary. \[ \left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{c} y \\ y \end{array}\right] \]