2 -3 -7 5 2 -2] [1 0 -2 1 1 -4 3 1 -4 2 1 3 1 -5 -7 6 2 -7 0 2 1 1 0 0 0 1 -2 -2 1 1 -1 A R= 0 0 0 0 0 0 |2 You may use, without justification, the fact that R is the reduced echelon form of A. Determine the set of all solutions to the linear system 2x1 – 3r2 – 7r3 + 5x4 + 2x5 = -2 ri – 2x2 – 4r3 + 3x4+ x5 = -2 2x1 – 4r3 + 2x4 +x5 = 3 2i – 5x2 – 7r3 + 6x4 + 2x5 = -7 and express this solution set in parametric vector form.

Given system of equation

$\left.\begin{array}{c}2x_1-3x_2-7x_3+5x_4+2x_5=-2\\ x_1-2x_2-4x_3+3x_4+x_5=-2\\ 2x_1-4x_3+2x_4+x_5=3\\ x_1-5x_2-7x_3+6x_4+2x_5=-7\end{array}\right\}\mathrm{.......}\left(1\right)$

Write the matrix form $Ax=b$

$\begin{array}{c}Ax=b\\ \left[\begin{array}{ccccc}2& -3& -7& 5& 2\\ 1& -2& -4& 3& 1\\ 2& 0& -4& 2& 1\\ 1& -5& -7& 6& 2\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\\ x_4\\ x_5\end{array}\right]=\left[\begin{array}{c}-2\\ -2\\ 3\\ -7\end{array}\right]\end{array}$

Write the augmented matrix $\left(A|b\right)$

$\left(A|b\right)=\left[\begin{array}{cccccc}2& -3& -7& 5& 2& -2\\ 1& -2& -4& 3& 1& -2\\ 2& 0& -4& 2& 1& 3\\ 1& -5& -7& 6& 2& -7\end{array}\right]$