# Exercise Set 1.1 – No. 6

6. Fnd a linear system in the unknowns x1,x2,x3,…, that corresponds to the given augmented matrix.

$\large&space;{\color{Blue}&space;(a)&space;\begin{bmatrix}&space;0&space;&&space;3&space;&&space;-1&space;&&space;-1&space;&&space;-1\\&space;5&space;&&space;2&space;&&space;0&space;&&space;-3&space;&&space;-6&space;\end{bmatrix}&space;}$

Consider the matrix $\large&space;{\color{Blue}&space;A=&space;\begin{bmatrix}&space;0&space;&&space;3&space;&&space;-1&space;&&space;-1&space;&&space;-1\\&space;5&space;&&space;2&space;&&space;0&space;&&space;-3&space;&&space;-6&space;\end{bmatrix}&space;}$

We have that the linear system of two equations in the four unknowns x1, x2, x3, and x4 given by

$\large&space;{\color{Blue}&space;\begin{matrix}&space;3x_2-x_3-x_4&space;=&space;-1&space;\\&space;5x_1+2x_2-3x_4&space;=&space;-6&space;\end{matrix}&space;}$

has A as its augmented matrix.

$\large&space;{\color{Blue}&space;(b)&space;\begin{bmatrix}&space;3&space;&&space;0&space;&&space;1&space;&&space;-4&space;&&space;3\\&space;-4&space;&&space;0&space;&&space;4&space;&&space;1&space;&&space;-3\\&space;-1&space;&&space;3&space;&&space;0&space;&&space;-2&space;&&space;-9\\&space;0&space;&&space;0&space;&&space;0&space;&&space;-1&space;&&space;-2&space;\end{bmatrix}&space;}$

Consider the matrix $\large&space;{\color{Blue}&space;A=&space;\begin{bmatrix}&space;3&space;&&space;0&space;&&space;1&space;&&space;-4&space;&&space;3\\&space;-4&space;&&space;0&space;&&space;4&space;&&space;1&space;&&space;-3\\&space;-1&space;&&space;3&space;&&space;0&space;&&space;-2&space;&&space;-9\\&space;0&space;&&space;0&space;&&space;0&space;&&space;-1&space;&&space;-2&space;\end{bmatrix}&space;}$

We have that the linear system of two equations in the four unknowns x1, x2, x3, and x4 given by

$\large&space;{\color{Blue}&space;\begin{matrix}&space;3x_1+x_3-4x_4&space;=&space;3&space;\\&space;-4x_1+4x_3+x_4&space;=&space;-3&space;\\&space;-x_1+3x_3-2x_4&space;=&space;-9&space;\\&space;-x_4&space;=&space;-2&space;\end{matrix}&space;}$

has A as its augmented matrix.