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