Inverse Of Matrix

R1C1

R = RowC = Column

3x3R2R3

C2 C3

A =35-2

det(A)= | A |

det = Determinant(A) = of A

| A | = Matrix

R1C1

-1 2

3 41 0

C2 C3

R3R2

1st We Find Determinant of Matrix

And then Co-Factor

A =

3 R1C1

3 4

1 0

C2 C3

R3

R2 5

-2

x

x

x x x

x

xA =

R1C1

4

0

C2 C3

R3

R2

x

A =

R1C1 C2 C3

R3

R25

-2

2

3

1

x x

xx

A =

R1C1 C2 C3

R3

R2

3 -1

3 4

1 0

2

-2

5

Plus sign minus sign Plus sign

-1

det(A)= | A |

det = Determinant(A) = of A

| A | = Matrix

3 41 0 5

-2 31

405

-2+3 -(-1) +2

3 41 0 5

-2 31

405

-2+3 -(-1) +2

--Now; Do Cross Multiply--+3(1x4-3x0)1(5x4+-2x0)+2(5x3+-2x1)3(4-0) +1(20-

0)+2(15-2)+3(4)+1(20)+2(17)12+20+34

As the value of Determinant is

= 66

2nd Find Co-Factor of MatrixR1

C1 C2

R3

R2

3 -1

3 4

1 0

2

-2

5

C34

1 0

3 4

0

-2

5

3

1

-2

5

-1

3 4

2 342

-23 -1

3-2

-102

1

302

53

1-1

5Use 1st place Plus(+) and 2nd place minus(-); and continue it till last!

+ - +

- + -

+ - +

--Do Cross Multiply and Solve--

17-204

-71610

810-2

4

8

-- Reflect the value Diagonal and Inverse the value (n)--n

2

n7

n4

n3n5n

8

16

4

8

16

n4n

2n3

n7

n8

n5

17-204

-71610

810-2

-2104

1016-20

8-717

-- Original values --

-- Interchange Values--

-2104

1016-20

8-717

Remember Determinant, use it

66

66

1

-1 = Inverse

= A-1

-2/6610/664/66

10/6616/66-20/66

8/66-7/6617/66

-1/335/332/33

5/338/33-10/33

4/33-7/3317/33

Use 1 over 66

A-1=

Divide values :

= A-1

We found Our inverse Matrix