A **Linear Equation can be represented in matrix** form using a:

- Coefficient Matrix
- Variable Matrix and
- Constant Matrix

The System of linear equation in three variables,

a1x+b1y+c1z=d1
a2x+b2y+c2z=d2
a3x+b3y+c3z=d3

The Matrix Representation would be

a1 b1 c1 xd1
a2 b2 c2y =d2
a3 b3 c3 zd3

We generalize the result of n variable

a1 b1 c1
a2 b2 c2 __ Coefficient Matrix
a3 b3 c3
x,y,z are Variable Matrix
d1,d2,d3 are Constant Matrix

Consider the System,

x+2y+3z=4
5x+6y+7z=8
8x+7y+6z=5

Then, the coefficient matrix for the above system is

1 2 3
5 6 7
8 7 6

Variable Matrix are X, Y, Z

Constant Matrix are 4,8,5

Representing of linear Matrix in above System is:

1 2 3 x 4
5 6 7 y = 8
8 7 6 z 5

## C++ program to implement the Representation of Linear Equation in Matrix form

OutputApplications:Systems of Linear Equations can be used to solve some

Real – Time Problems: