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Solve the system of equations x?2y?z?2t=1 3x?5y?2z?3t=2 2x?5y?2z?5t=3 ?x+4y+4z+11t= ?1 Using Gauss-Jordan to Solve a System

Solve the system of equations

x?2y?z?2t=1

3x?5y?2z?3t=2

2x?5y?2z?5t=3

?x+4y+4z+11t= ?1

Using Gauss-Jordan to Solve a System

Expert Solution

The augmented matrix for the given system of equations is A (say)=

1	-2	-1	-2	1
3	-5	-2	-3	2
2	-5	-2	-5	3
-1	4	4	11	-1

To solve the given system of equations, we will reduce A to its RREF as under:

Add -3 times the 1st row to the 2nd row

Add -2 times the 1st row to the 3rd row

Add 1 times the 1st row to the 4th row

Add 1 times the 2nd row to the 3rd row

Add -2 times the 2nd row to the 4th row

Add -1 times the 3rd row to the 4th row

Add -2 times the 4th row to the 3rd row

Add -3 times the 4th row to the 2nd row

Add 2 times the 4th row to the 1st row

Add -1 times the 3rd row to the 2nd row

Add 1 times the 3rd row to the 1st row

Add 2 times the 2nd row to the 1st row

Then the RREF of A is

1	0	0	0	-5
0	1	0	0	-3
0	0	1	0	-4
0	0	0	1	2

Hence, x = -5,y = -3,z= -4 and t = 2.

milcah answered 1 year ago

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