Chapter 7.4, Problem 50E

To determine

To write: the system of linear equation corresponding to the given augmented matrix and find the solution.

Answer to Problem 50E

The system of linear equation corresponding to the given augmented matrixis

  $\{\begin{array}{l}x+8y=12\\ y=3\end{array}$

The solution is given by $x=-12,y=3$ .

Explanation of Solution

Given information:

An augmented matrix is given as

  $\left[\begin{array}{cccc}1& 8& ⋮& 12\\ 0& 1& ⋮& 3\end{array}\right]$

Concept used:

Co-efficient matrix of a system of linear equation of the form $\{\begin{array}{l}{a}_{1}x+b_{1}y=c_1\\ a_{2}x+b_{2}y=c_2\end{array}$ is given by

  $\left[\begin{array}{cc}{a}_1& b_1\\ a_2& b_2\end{array}\right]$

The augmented matrix of the system of linear equation is given by

  $\left[\begin{array}{cccc}{a}_1& b_1& ⋮& c_1\\ a_2& b_2& ⋮& c_2\end{array}\right]$

Consider the given matrix.

  $\left[\begin{array}{cccc}1& 8& ⋮& 12\\ 0& 1& ⋮& 3\end{array}\right]$

Now, the corresponding system of equation will be

  $\{\begin{array}{l}x+8y=12\\ y=3\end{array}$

Variables x , y have been used with the coefficients.

Now, substitute back $y=3$ in $x+8y=12$ .

  $\begin{array}{c}x+8y=12\\ x+8\left(3\right)=12\\ x+24=12\\ x=-12\end{array}$

Therefore, solution of the system of linear equation is

  $x=-12,y=3$