Question

Dakarai wrote the system of linear equations below. 7x+8y=28 and -3x+9y=-24 Dakarai then wrote the coefficient Matrix that represented this system. Which Matrix could she have written?
7 8
-3 9

7 -3
8 9

7 8 28
-3 9 -24

7 -3 28
8 9 -24

Answer 1

The system of linear equations $a_1x+b_1y=c_1\\a_2x+b_2y=c_2$

can be represented in the form of the Matrix as $AX=B$

Where $A=\begin{pmatrix} a_1 &b_1 \\a_2 &b_2 \end{pmatrix}\\X=\begin{pmatrix} x\\y \\\end{pmatrix}\\ B=\begin{pmatrix} c_1\\c_2 \\\end{pmatrix}$

The matrix A is called the coefficient matrix of the system of linear equations.

Here the given system of linear equation as:

$7x+8y=28 \\ -3x+9y=-24$

The matrix form of the given system of equation as

$A=\begin{pmatrix} 7 &8 \\-3 &9 \end{pmatrix}\\B=\begin{pmatrix} 28\\-24 \\\end{pmatrix}\\X=\begin{pmatrix} x\\y \\\end{pmatrix}$

The coefficient matrix of A is $A=\begin{pmatrix} 7 &8 \\-3 &9 \end{pmatrix}$