Q. 22 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 20–25, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.

$\left\{\begin{array}{r}2x+y+z=5\\ 4x-y-3z=1\\ 8x+y-z=5\end{array}\right.$

Step-by-Step Solution

Answer

The system of equations has no solution or the equations are inconsistent.

Step 1. Given information

The given system of equations is $\left\{\begin{array}{r}2x+y+z=5\\ 4x-y-3z=1\\ 8x+y-z=5\end{array}\right.$

Step 2. Solve system of equations using matrix

$A=\left[\begin{array}{ccc}2& 1& 1\\ 4& -1& -3\\ 8& 1& -1\end{array}\right],X=\left[\begin{array}{l}x\\ y\\ z\end{array}\right], B=\left[\begin{array}{l}5\\ 1\\ 5\end{array}\right]$

$$\begin{gathered} AX=B \\ X=A^{-1}B \end{gathered}$$

The inverse of the matrix $A$ does not exist. Therefore, the system of equations has no solution or the equations are inconsistent.