SOLVING SYSTEMS OF EQUATIONS USING INVERSE MATRICES

Solve the following system of linear equations by matrix inversion method.

Problem 1 :

2x + 5y = -2 and x + 2y = -3

Solution :

By applying the value of |A| and adj A, we get

So, the solution is x = -11 and y = 4.

Problem 2 :

2x - y = 8, 3x + 2y = -2

Solution :

By applying the value of |A| and adj A, we get

So, the solution is x = 2 and y = -4.

Problem 3 :

2x + 3y - z = 9; x + y + z = 9 and 3x - y - z = -1

Solution :

Finding adjoint matrix :

x = 32/16 ==> 2

y = 48/16 ==> 3

z = 64/16 ==> 4

So, the solution is (2, 3, 4).

Problem 4 :

x + y + z - 2 = 0, 6x - 4y + 5z - 31 = 0, 5x + 2y + 2z = 13

Solution :

Finding adjoint of matrix :

Solving for x, y and z.

x = 81/27 ==> 3

y = 0/27 ==> 0

z = 27/27 ==> 1

So, the solution is (3, 0, 1).

Problem 5 :

If

find the products AB  and BA and hence solve the system of equations x + y + 2z = 1, 3x + 2y + z = 7, 2x + y + 3z = 2

Solution :

Finding the product of matrices :

Finding |A| :

Finding adjoint of matrix :

Solving the system of equations using formula :

x = 2, y = 1 and z = -1

So, the solution is (2, 1, -1).