Inverse of matrix

Inverse Of Matrix

By:= Jitendra thakor

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…

Inver se Of M

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Example…

4 2 3

8 3 5 .

7 2 4

A

− = − −

Inver se Of M

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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.

~

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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 ~

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Step 3: Then make second and third element of first row 0 using column operation.

R2 – R1 & R3 – 3R1

~

C2 + 2C1 &C3 – C1

~

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Step 4: Make second element of second row 1.

R2 – R3 ~

-1R2 ~

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R3 – 4R2~

R2 – R3 ~

Step 5: Make 0 above and below of second element of second row.

Step 6: Take column operation.

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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.

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10

Questions…???

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