by using a system of linear equations Balance a chemical rea

by using a system of linear equations.

Balance a chemical reactionNaOH + H_{2}SO_{4} \ ightarrow Na_{2}SO_{4} + H_{2}O by using a system of linear equations.

Solution

Find the pivot in the 1st column in the 1st row

Subtract the 1st row from the 2nd

Subtract the 1st row from the 4th

Find the pivot in the 2nd column and swap the 3rd and the 2nd rows

Multiply the 2nd row by 4

Subtract the 2nd row from the 3rd row and restore it

Multiply the 2nd row by 2

Subtract the 2nd row from the 4th row and restore it

Make the pivot in the 3rd column by dividing the 3rd row by 2

Multiply the 3rd row by -2

Subtract the 3rd row from the 1st row and restore it

Multiply the 3rd row by -1

Subtract the 3rd row from the 2nd row and restore it

Multiply the 3rd row by 4

Subtract the 3rd row from the 4th row and restore it

x1 = x4

x2 = (1/2)x4

x3 = (1/2)x4

(1,1/2,1/2,1) multiply with 2 we will get (2,1,1,2)
so we will have   2NaOH+H2sO4-> Na2 so4+2H20

	X1	X2	X3	X4	b
1	1	0	-2	0	0
2	1	4	-4	-1	0
3	0	1	-1	0	0
4	1	2	0	-2	0