Chapter 11, Problem 6CT

To determine

The system of equation corresponding to the augmented matrix $\left[\begin{array}{cccc}3& 2& 4& -6\\ 1& 0& 8& 2\\ -2& 1& 3& -11\end{array}\right]$.

Answer to Problem 6CT

Solution:

The system of equation corresponding to the augmented matrix $\left[\begin{array}{cccc}3& 2& 4& -6\\ 1& 0& 8& 2\\ -2& 1& 3& -11\end{array}\right]$ is

$\{\begin{array}{l}3x+2y+4z=-6\\ x+8z=2\\ -2x+y+3z=-11\end{array}$.

Explanation of Solution

Given information:

The augmented matrix, $\left[\begin{array}{cccc}3& 2& 4& -6\\ 1& 0& 8& 2\\ -2& 1& 3& -11\end{array}\right]$

Explanation:

Consider the augmented matrix $\left[\begin{array}{cccc}3& 2& 4& -6\\ 1& 0& 8& 2\\ -2& 1& 3& -11\end{array}\right]$.

The matrix has three rows and represents a system with three equations. The three columns to the left of the vertical bar indicate that the system has three variables.

Let $x,y,z$ denotes three variables. The column to the right of the vertical bar represents the constants on the right side of the equations.

The system is

$\{\begin{array}{l}3x+2y+4z=-6\\ x+0y+8z=2\\ -2x+y+3z=-11\end{array}$

Which is equivalent to $\{\begin{array}{l}3x+2y+4z=-6\\ x+8z=2\\ -2x+y+3z=-11\end{array}$

Therefore, the system of equation corresponding to the augmented matrix $\left[\begin{array}{cccc}3& 2& 4& -6\\ 1& 0& 8& 2\\ -2& 1& 3& -11\end{array}\right]$ is

$\{\begin{array}{l}3x+2y+4z=-6\\ x+8z=2\\ -2x+y+3z=-11\end{array}$.