row echelon solve the system of linear equations whose 2 3 S

row echelon

solve the system of linear equations whose 2 3

Solution

The augmented matrix of the linear system of equations is A =

0

2

3

8

2

3

1

5

1

-1

-2

-5

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

Interchange the 1st row and the 2nd row

Multiply the 1st row by ½

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

Multiply the 2nd row by 1/2

Add 5/2 times the 2nd row to the 3rd row

Multiply the 3rd row by 4/5        

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

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

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

Then, the RREF of A is

1

0

0

0

0

1

0

1

0

0

1

2

Now, the solution of the given linear system of equations is x = 0, y = 1 and z = 2.

0	2	3	8
2	3	1	5
1	-1	-2	-5