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Question 9 - Inverse of matrix using elementary transformation - Chapter 3 Class 12 Matrices
Last updated at Dec. 16, 2024 by Teachoo
Inverse of matrix using elementary transformation
Elementary operations on a matrix
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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
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Inverse of matrix using elementary transformation
- Proof using mathematical induction
Transcript
Ex3.4, 9 Find the inverse of each of the matrices, if it exist [ 8(3&10@2&7)] Let A = [ 8(3&10@2&7)] We know that A = IA [ 8(3&10@2&7)]= [ 8(1&0@0&1)] A R1 R1 R2 [ 8( &10 7@2&7)]= [ 8(1 0&0 1@0&1)] A [ 8( &3@2&7)]= [ 8(1& 1@0&1)] A R2 R2 2R1 [ 8(1&3@ ( )&7 2(3))]= [ 8(1& 1@0 2(1)&1 2( 1))] A [ 8(1&3@ &7 6)]= [ 8(1& 1@0 2&1+2)] A [ 8(1&3@ &1)]= [ 8(1& 1@ 2&3)] A R1 R1 3R2 [ 8(1 3(0)& ( )@0&1)]= [ 8(1 3( 2)& 1 3(3)@ 2&3)] A [ 8(1 0& @0&1)]= [ 8(1+6& 1 9@ 2&3)] A [ 8(1& @0&1)]= [ 8(7& 10@ 2&3)] A I = [ 8(7& 10@ 2&3)] A This is similar to I = A-1 A Thus A-1 =[ 8(7& 10@ 2&3)]
