Chapter 3.4, Problem 28HP

To determine

To describe:

The system of equations by using the given graph.

Explanation of Solution

Given:

  $A$ Be the matrix of coefficients for a given system.

Concept used:

The system in a matrix form

  $AX=b$

Where $X$ is the vector of unknowns and $b$ the vector of constants from the right side of the equation?

Calculation:

The system in a matrix form

  $AX=b\mathrm{...............}\left(1\right)$

If matrix $A$ invertible, compute $A^{-1}$ and multiply the equation $\left(1\right)$ with $A^{-1}$ on the left.

  $A^{-1}AX=A^{-1}b$

Since $A^{-1}A=I$

Where $I$ is the unit matrix?

  $A^{-1}b=X$

So, solving the system consists in multiplying the inverse by the constants vector.

The solution for a system of inequalities in three variables are include the region of planes in which the individual solutions of each inequality overlap.