Explanation:
Let the argumented matrix:
[ 3-1 +9]
[ 2+1 -4]
We solve the matrix by Gauss- Jordan Eleminating:
Let denote the above matrix like A.
Let the denote the row by 1 by R1 =[3 -1 | +9]
And let denote rhe row 2 by R2= [ 2 +1 | -4]
So, we will apply the elementary operations per row
First operation: R2=3 R2, then [-3 -9| 9]
[ 6 3| -72]
Second operation: R2 = R2/ 2
[ 3 -7| 9]
[ 3 3/2 | -6]
Now, R2 = R2 - R1
[3 -7| 9 ]
[0 5/2 | -15]
R2=R2÷(5/2), That is :
R1=R1/3
R1=R1+( 1/3) R2
That Is : + (1/3) R2
That is :
[1 0| 1]
[ 0 1| -6]
So the above- argumented matrix is equivalent to the following linear system of equations:
1x +0 y =1
0x+1y= -6
That is
x=1
y= -6
One solution for the matrix A is (1, -6)
The correct solution will be ( 1, -5)