Question

Solve + + = , + + = , + − = using matrix inversion method.​

Answer 1

Answer:

Example 1.22

Solve the following system of linear equations, using matrix inversion method:

5x + 2 y = 3, 3x + 2 y = 5 .

Solution

The matrix form of the system is AX = B , where

We find |A| = = 10 - 6= 4 ≠ 0. So, A−1 exists and A−1 =

Then, applying the formula X = A−1B , we get

So the solution is (x = −1, y = 4).

Example 1.23

Solve the following system of equations, using matrix inversion method:

2x1 + 3x2 + 3x3 = 5,

x1 – 2x2 + x3 = -4,

3x1 – x2 – 2x3 = 3

Solution

The matrix form of the system is AX = B,where

So, the solution is ( x1 = 1, x2 = 2, x3 = −1) .

Example 1.24

If , find the products AB and BA and hence solve the system of equations x − y + z = 4, x – 2y – 2z = 9, 2x + y +3z =1.

Solution

Writing the given system of equations in matrix form, we get

Hence, the solution is (x = 3, y = - 2, z = −1).