# Example 24 - Chapter 3 Class 12 Matrices

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Example 24 Obtain the inverse of the following matrix using elementary operations A = [ 8(0&1&2@1&2&3@3&1&1)] Given A = [ 8(0&1&2@1&2&3@3&1&1)] We know that A = IA [ 8(0&1&2@1&2&3@3&1&1)] = [ 8(1&0&0@0&1&0@0&0&1)] A R1 R2 [ 8( &2&3@0&1&2@3&1&1)] = [ 8(0&1&0@1&0&0@0&0&1)] A R3 R3 3R1 [ 8(1&2&3@0&1&2@ ( )&1 3(2)&1 3(3))] = [ 8(0&1&0@1&0&0@0 3(0)&0 3(1)&1 3(0))]A [ 8(1&2&3@0&1&2@ & 5& 8)] = [ 8(0&1&0@1&0&0@0& 3&1)] R1 R1 2R2 [ 8(1 2(0)& ( )&3 2(2)@0&1&2@0& 5& 8)] = [ 8(0 2(1)&1 2(0)&0 2(0)@1&0&0@0& 3&1)]A [ 8(1& & 1@0&1&2@0& 5& 8)] = [ 8( 2&1&0@1&0&0@0& 3&1)] A R3 R3 + 5R2 [ 8(1&0& 1@0&1&2@0+5(0)& + ( )& 8+5(2))] = [ 8( 2&1&0@1&0&0@0+5(1)& 3+5(0)&1+5(0))] A [ 8(1&0& 1@0&1&2@0& &2)] = [ 8( 2&1&0@1&0&0@5& 3&1)] A R3 1/2 R3 [ 8(1&0& 1@0&1&2@0/2&0/2& / )] = [ 8( 2&1&0@1&0&0@5/2&( 3)/2&1/2)] A R1 R1 + R3 [ 8(1+0&0+0& + @0&1&2@0&0&1)]=[ 8( 2+5/2&1+(( 3)/2)&0+1/2@1&0&0@5/2&( 3)/2&1/2)] A [ 8(1&0& @0&1&2@0&0&1)] = [ 8(1/2&( 1)/2&1/2@1&0&0@5/2&( 3)/2&1/2)] A R2 R2 2R3 [ 8(1&0&0@0 2(0)&1 2(0)& ( )@0&0&1)] = [ 8(1/2&( 1)/2&1/2@1 2(5/2)&0 2(( 3)/2)&0 2(1/2)@5/2&( 3)/2&1/2)]A [ 8(1&0&0@0&1& @0&0&1)] = [ 8(1/2&( 1)/2&1/2@ 4&3& 1@5/2&( 3)/2&1/2)] A I= [ 8(1/2&( 1)/2&1/2@ 4&3& 1@5/2&( 3)/2&1/2)] A This is similar to I = A-1 A Hence A-1 = [ 8(1/2&( 1)/2&1/2@ 4&3& 1@5/2&( 3)/2&1/2)]

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Example 24 You are here

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.