Misc. 6 - Chapter 3 Class 12 Matrices

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Misc. 6 Find the values of x, y, z if the matrix A = [ 8(0&2 & @ & & @ & & )] satisfy the equation A A = I. Given, A = [ 8(0&2 & @ & & @ & & )] A = [ 8(0& & @2 & & @ & & )] I = [ 8(1&0&0@0&1&0@0&0&1)] Now, A A = I Putting values [ 8(0& & @2 & & @ & & )][ 8(0&2 & @ & & @ & & )] = [ 8(1&0&0@0&1&0@0&0&1)] [ 8(0(0)+ ( )+ ( )&0(2 )+ ( )+ ( )&0( )+ ( )+ ( )@2 (0)+ ( ) ( )&2 (2 )+ ( ) ( )&2 ( )+ ( ) ( )@ (0) ( )+ ( )& (2 ) ( )+ ( )& ( ) ( )+ ( ))] = [ 8(1&0&0@0&1&0@0&0&1)] [ 8(0+ ^2+ ^2&0+ &0 + @0+ &4 ^2+ ^2+ ^2&2 @0 + &2 & ^2+ ^2+ ^2 )]= [ 8(1&0&0@0&1&0@0&0&1)] [ 8(2 ^2&0&0@0&6 ^2&0@0&0&3 ^2 )]= [ 8(1&0&0@0&1&0@0&0&1)] Since matrices are equal, corresponding elements are equal Thus, x = 1/ 2 , y = 1/ 6 , z = 1/ 3