Q. 14 - Precalculus Enhanced with Graphing Utilities

Question

solve each system of equations using matrices.

If the system has no solution, say that it is inconsistent.

$$\begin{gathered} x+\frac{1}{4}y=7 \\ 8x+2y=56 \end{gathered}$$

Step-by-Step Solution

Answer

The given equation is inconsistent therefore no solution exists.

Step 1. Given

$$\begin{gathered} x+\frac{1}{4}y=7 \\ 8x+2y=56 \end{gathered}$$

Step 2. Calculation

$$\begin{gathered} For an equation AX=B \\ when we find A^{-1} \\ we multiply it with the current expression i.e. \\ {A}^{-1}AX=A^{-1}B \\ IX=A^{-1}B \\ X=A^{-1}B \\ Since given matrix is \sin gular thus the inverse can\text{'}t be obtained. \end{gathered}$$