basic example about ,Inverse Of Matrix,how to get Inverse Of Matrix

1. Inverse Of Matrix
By:=
Jitendra thakor

2. Gauss-Jordan Method for Inverses
Step 1: Write down the matrix A, and on its right write
an identity matrix of the same size.
Step 2: Perform elementary row operations on the
left-hand matrix so as to transform it into an
identity matrix. These same operations are
performed on the right-hand matrix.
Step 3: When the matrix on the left becomes an
identity matrix, the matrix on the right is the
desired inverse.
Main Procedure…
InverseOfMatrix

3. Example…
4 2 3
8 3 5 .
7 2 4
A
− 
 = − 
 − 
InverseOfMatrix

4. 4 2 3 1 0 0
8 3 5 0 1 0
7 2 4 0 0 1
 −
 
− 
 − 
4 2 3
8 3 5 .
7 2 4
A
− 
 = − 
 − 
Step 1: First take identity matrix of same size on it’s
right side.
~
InverseOfMatrix

5. Step 2: In this step we want to make first element of
first raw 1 and make 0 below this first element.
So take
R2-2R1 ~
C1 - C3 ~
InverseOfMatrix

6. Step 3: Then make second and third element of first
row 0 using column operation.
R2 – R1 &
R3 – 3R1
~
C2 + 2C1 &
C3 – C1
~
InverseOfMatrix

7. Step 4: Make second element of second row 1.
R2 – R3 ~
-1R2 ~
InverseOfMatrix

8. R3 – 4R2
~
R2 – R3
~
Step 5: Make 0 above and below of second element
of second row.
Step 6: Take column operation.
InverseOfMatrix

9. So A-1
=
-1R3 ~
Step 7: Make third element of third row 1.
So the matrix right hand side of identity matrix is
inverse of given matrix.
InverseOfMatrix

10. 10
Questions…???
InverseOfMatrix