Chapter 3, Problem 3SGR

To determine

To fill the blank space: A matrix that contains the constants in a system of equations is called a(n)……constant matrix…………….

Answer to Problem 3SGR

A matrix that contains the constants in a system of equations is called a……constant matrix…………….

Explanation of Solution

Given information :

Given a matrix that contains the constants in a system of equations.

Consider a simple linear system of equations $a_{1}x+a_{2}y=b_{1}and{a}_{3}x+a_{4}y=b_2$ having $2$ equations with $2$ unknowns.

Where $a_1,a_3,and{a}_2,a_4$ are coefficients of $x,y-$ respectively and $b_1,b_2$ are constant terms of the given two equations.

The above two equations represented as $AX=B$ in matrix form.

Where $A=\left[\begin{array}{cc}{a}_1& a_2\\ a_3& a_4\end{array}\right]$ is called coefficient matrix as it contains coefficient of given equations,

  $X=\left[\begin{array}{l}x\\ y\end{array}\right]$ is called variables matrix as it contains variables of given equations and $B=\left[\begin{array}{l}{b}_1\\ b_2\end{array}\right]$ is called constant matrix as it contains constant values of given equations.

Hence, a matrix that contains the constants in a system of equations is called a constant matrix.