Matrix Inverse Example Calutation from determinant, adjoint Tutorial, formula.

Inverse of Matrix - Tutorial

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>> Matrix Inverse & Adjoint Calculator.

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>> Find Inverse of matrix
>> Find determinant of A (|A|)
>> Find adjoint of A (adj A)

Inverse of Matrix

Inverse of Matrix :
After calculating determinant, adjoint from the matrix as in the previous tutorials a) Find determinant of A (|A|)
b) Find adjoint of A (adj A)

we will be calculating the inverse using determinant and adjoint
c) Calculate the inverse using the formulae
A^-1 = adjoint A / |A|
An Example:
For an example we will find the inverse for the following matrix

Matrix A

1	3	1
1	1	2
2	3	4

a)Finding determinant of A:
|A| = 1x(1x4-3x2) - 3x(1x4-2x2) + 1x(1x3-2x1)
|A| = 1x(4-6) - 3x(4-4) + 1x(3-2) = -2+0+1
|A| = -1

b)Finding Minors of A:
M₁₁ = 1x4-3x2 = 4-6 = -2
M₁₂ = 1x4-2x2 = 4-4 = 0
M₁₃ = 1x3-2x1 = 3-2 = 1
M₂₁ = 3x4-3x1 = 12-3 = 9
M₂₂ = 1x4-2x1 = 4-2 = 2
M₂₃ = 1x3-2x3 = 3-6 = -3
M₃₁ = 3x2-1x1 = 6-1 = 5
M₃₂ = 1x2-1x1 = 2-1 = 1
M₃₃ = 1x1-1x3 = 1-3 = -2

c)Forming Minors Matrix of A:

Matrix of minors

-2	0	1
9	2	-3
5	1	-2

d)Forming Cofactor Matrix of A:

Matrix of cofactors

-2 x 1	0 x -1	1 x 1
9 x -1	2 x 1	-3 x -1
5 x 1	1 x -1	-2 x 1

-2	0	1
-9	2	3
5	-1	-2

e)Forming Adjoint A:

Adjoint Matrix (Adj A)

-2	-9	5
0	2	-1
1	3	-2

f) Finding the Inverse Matrix of A

Inverse of Matrix (A^-1)

A^-1 = ajd A / |A| =

1/-1

-2	-9	5
0	2	-1
1	3	-2

A^-1

2	9	-5
0	-2	1
-1	-3	2

Related Calculator:
>> Matrix Inverse & Adjoint Calculator.

Related Topics:
>> Find Inverse of matrix
>> Find determinant of A (|A|)
>> Find adjoint of A (adj A)