Inverse of matrix using elementary transformation

Chapter 3 Class 12 Matrices
Concept wise

### 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

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#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.