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Question 5 - 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, 5 Find the inverse of each of the matrices, if it exists. [ 8(2&1@7&4)] Let A = [ 8(2&1@7&4)] We know that A = IA [ 8(2&1@7&4)] = [ 8(1&0@0" " &1)] A R1 R1 1/7 R2 [ 8( / ( )&1 1/7(4)@7&4)] = [ 8(1 1/7(0)&0 1/7(1)@0" " &1)] A [ 8( &1 4/7@7&4)] = [ 8(1 0&( 1)/7@0" " &1)] A [ 8( &3/7@7&4)] = [ 8(1&( 1)/7@0" " &1)] A R2 R2 7R1 [ 8(1&3/7@ ( )&4 7(3/7) )] = [ 8(1&( 1)/7@0 7(1)&1 7(( 1)/7) )] A [ 8(1&3/7@ &4 3)] = [ 8(1&( 1)/7@0 7&1+1)] A [ 8(1&3/7@ &1)] = [ 8(1&( 1)/7@ 7&2)] A R1 R1 3/7R2 [ 8(1 3/7(0)& / / ( )@0&1)] = [ 8(1 3/7( 7)&( 1)/7 3/7(2)@ 7&2)] A [ 8(1 0& / / @0&1)] = [ 8(1+3&( 1)/7 6/7@ 7&2)] A [ 8(1& @0&1)] = [ 8(4& 1@ 7" " &2)] A I = [ 8(4& 1@ 7" " &2)] A This is similar to I = A-1A Thus, A-1 = [ 8(4& 1@ 7" " &2)] A
