USING MATRIX INVERSE TO SOLVE A SYSTEM OF 3 LINEAR EQUATIONS

Example 1 :

Solve the following linear equation by inversion method

2x + y + z = 5

x + y + z = 4

x - y + 2z = 1

Solution :

First we have to write the given equation in the form

AX = B

Here X represents the unknown variables. A represent coefficient of the variables and B represents constants.

To solve this we have to apply the formula X = A⁻¹ B

|A|  =  2 [2-(-1)] - 1 [2-1] +1 [-1-1]

      =  2 [2+1] - 1 [1] +1 [-2]

      =  2 [3] - 1 -2

      =  6 - 3

      =  3

|A| = 3 ≠ 0

Since A is a non singular matrix. A⁻¹ exists. 

x  =  3, y  =  6 and z  =  3

Example 2 :

Solve the following linear equation by inversion method

x + 2y + z = 7

2x - y + 2z = 4

x + y - 2z = -1

Solution :

To solve this we have to apply the formula X = A⁻¹ B

|A|  =  2 [2-2] -2[-4-2]+1[2+1]

=  2(0) - 2(-6) + 1(3)

=  0+12+3

|A|  =  15 ≠ 0

Since A is a non singular matrix. A⁻¹ exists. 

Example 3 :

Solve the following linear equation by inversion method

2x + y + z = 5

x + y + z = 4

x - y + 2z = 1 

Solution :

To solve this we have to apply the formula X = A⁻¹ B

  =  2(2+1)+1(2-1)+1(-1-1)

  =  2(3)-1-2

  =  3

|A|  =  3  ≠  0

Since A is a non singular matrix. A⁻¹ exists

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