# Ex 3.4, 17 - Chapter 3 Class 12 Matrices

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex3.4, 17 Find the inverse of each of the matrices, if it exists. [ 8(2&0& 1@5&1&0@0&1&3)] Let A =[ 8(2&0& 1@5&1&0@0&1&3)] We know that A = IA [ 8(2&0& 1@5&1&0@0&1&3)]= [ 8(1&0&0@0&1&0@0&0&1)] A R1 1/2 R1 , [ 8( / &0/2&( 1)/2@5&1&0@0&1&3)]= [ 8(1/2&0/2&0/2@0&1&0@0&0&1)] A [ 8( &0& 1/2@5&1&0@0&1&3)] = [ 8(1/2&0&0@0&1&0@0&0&1)] A R2 R2 5R1 [ 8(1&0& 1/2@ ( )&1 5(0)&0 5(( 1)/2)@0&1&3)] = [ 8(1/2&0&0@0 5(1/2)&1 5(0)&0 5(0)@0&0&1)] A [ 8(1&0& 1/2@ &1&5/2@0&0&3)]= [ 8(1/2&0&0@ 5/2&1&0@0&0&1)] A R3 R3 R2 [ 8(1&0& 1/2@0&1&5/2@ &0&3 5/2)]= [ 8(1/2&0&0@ 5/2&1&0@0 ( 5/2)&0 1&1 0)] A [ 8(1&0& 1/2@0&1&5/2@ &0&1/2)]= [ 8(1/2&0&0@ 5/2&1&0@5/2& 1&1)] A R3 2R3 [ 8(1&0& 1/2@0&1&5/2@2 0&2 0& / )]= [ 8(1/2&0&0@ 5/2&1&0@2 5/2&2 ( 1)&2(1))] A [ 8(1&0& 1/2@0&1&5/2@0&0& )]= [ 8(1/2&0&0@ 5/2&1&0@5& 2&2)] A R1 R1 + 1/2 R3 [ 8(1+1/2(0)&0+1/2(0)&( )/ + / ( )@0&1&5/2@0&0&1)]= [ 8(1/2+1/2(5)&0+1/2( 2)&0+1/2(2)@( 5)/2&1&0@5& 2&2)] A [ 8(1&0& @0&1&5/2@0&0&1)]= [ 8(3& 1&1@( 5)/2&1&0@5& 2&2)] A R2 R2 5/2 R3 [ 8(1&0&0@0 5/2(0)&1 5/2(0)& / / ( )@0&0&1)]= [ 8(3& 1&1@( 5)/2 5/2 (5)&1 5/2( 2)&0 5/2@5& 2&2)] A [ 8(1&0&0@0&1& @0&0&1)]= [ 8( 3& 1&1@( 30)/2&6& 5@5& 2&2)] A "I"= [ 8( 3& 1&1@ 15&6& 5@5& 2&2)] A This is similar to I = A-1A Thus, A-1 = [ 8(3& 1&1@ 15&6& 5@5& 2&2)]

Inverse of matrix using elementary transformation

Elementary operations on a matrix

Inverse of a matrix

Finding inverse of a matrix using Elementary Operations

Ex 3.4, 18

Example 23

Example 25

Ex 3.4, 1

Ex 3.4, 2

Ex 3.4, 3

Ex 3.4, 4

Ex 3.4, 5

Ex 3.4, 6

Ex 3.4, 7

Ex 3.4, 8

Ex 3.4, 9

Ex 3.4, 10

Ex 3.4, 11

Ex 3.4, 12

Ex 3.4, 13

Ex 3.4, 14

Example 24

Ex 3.4, 15 Important

Ex 3.4, 16

Ex 3.4, 17 Important You are here

Chapter 3 Class 12 Matrices

Concept wise

- Formation and order of matrix
- Types of matrices
- Equal matrices
- Addition/ subtraction of matrices
- Statement questions - Addition/Subtraction of matrices
- Multiplication of matrices
- Statement questions - Multiplication of matrices
- Solving Equation
- Finding unknown - Element
- Finding unknown - Matrice
- Transpose of a matrix
- Symmetric and skew symmetric matrices
- Proof using property of transpose
- Inverse of matrix using elementary transformation
- Proof using mathematical induction

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.