Inverse of matrix
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Transcript of Inverse of matrix
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