Question

Solve the following system of equations by matrix method:

(i) 3x + 7y = 4

x + 2y = -1

(ii) 3x + y = 7

5x + 3y = 12

Answer 1

(i) Given as

3x + 7y = 4

x + 2y = -1

Above equation can be written as

Here

|A| = 6 - 7 = - 1

Therefore, the above system has unique solution given as

X = A-1B

Suppose Cij be the cofactor of aij in A

So, X = -15 and Y = 7

(ii) Given as

3x + y = 7

5x + 3y = 12

Above equation can be written as

Here

|A| = 9 - 5 = 4

Therefore, the above system has unique solution given as

X = A-1B

Suppose Cij be the cofactor of aij in A

So, x = 9/4 and y = 1/4