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Ex 3.4, 5 - Chapter 3 Class 12 Matrices (Term 1)

Last updated at March 16, 2023 by

Ex 3.4, 5 - Find inverse [2 1 7 4] - Chapter 3 Class 12 - Ex 3.4

Ex 3.4, 5 - Chapter 3 Class 12 Matrices - Part 2
Ex 3.4, 5 - Chapter 3 Class 12 Matrices - Part 3

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Ex3.4, 5 Find the inverse of each of the matrices, if it exists. [ 8(2&[email protected]&4)] Let A = [ 8(2&[email protected]&4)] We know that A = IA [ 8(2&[email protected]&4)] = [ 8(1&[email protected]" " &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/[email protected]&4)] = [ 8(1 0&( 1)/[email protected]" " &1)] A [ 8( &3/[email protected]&4)] = [ 8(1&( 1)/[email protected]" " &1)] A R2 R2 7R1 [ 8(1&3/[email protected] ( )&4 7(3/7) )] = [ 8(1&( 1)/[email protected] 7(1)&1 7(( 1)/7) )] A [ 8(1&3/[email protected] &4 3)] = [ 8(1&( 1)/[email protected] 7&1+1)] A [ 8(1&3/[email protected] &1)] = [ 8(1&( 1)/[email protected] 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/[email protected] 7&2)] A [ 8(1& @0&1)] = [ 8(4& [email protected] 7" " &2)] A I = [ 8(4& [email protected] 7" " &2)] A This is similar to I = A-1A Thus, A-1 = [ 8(4& [email protected] 7" " &2)] A

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