Ex 3.2, 3 - Chapter 3 Class 12 Matrices

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Ex 3.2, 3 Compute the indicated products (i)[ 8(a&b@ b&a)] [ 8(a& b@b&a)] [ 8(a&b@ b&a)]_"2 2" [ 8(a& b@b&a)]_"2 2" = [ 8( a a+b b&a ( b)+b a@ b a+b b&( b) ( b)+a a)]_(2 2) = [ 8(a2+b2& ab+ab@ ab+ab&b2+a2)] = [ 8(a2+b2&0@0&b2+a2)] Ex 3.2, 3 Compute the indicated products (ii)[ (1@2@3)][2 3 4] [ (1@2@3)]_(3 1)[2 3 4]1 3 = " " [ 8(1 2&1 3&1 4@2 2&2 3&2 4@3 2&3 3&3 4)] _(3 3) = [ 8(2&3&4@4&6&8@6&9&12)] Ex 3.2, 3 Compute the indicated products (iii) [ 8(1& 2@2&3)] [ 8(1&2&3@2&3&1)] [ 8(1& 2@2&3)]_"2 2" [ 8(1&2&3@2&3&1)]_"2 3" = [ 8(1 1+( 2) 2&1 2+( 2) 3&1 3+( 2) 1@2 1+3 2&2 2+3 3&2 3+3 1)]_(2 3) = [ 8(1 4&2 6&3 2@2+6&4+9&6+3)] = [ 8( 3& 4&1@8&13&9)] Ex 3.2, 3 Compute the indicated products (iv) [ 8(2&3&4@ (3@4)& (4@5)& (5@6))] [ 8(1& 3&5@ (0@3)& (2@0)& (4@5))] [ 8(2&3&4@ (3@4)& (4@5)& (5@6))]_(3 3) [ 8(1& 3&5@ (0@3)& (2@0)& (4@5))]_(3 3) = [ 8(2 1+3 0+4 3&2 ( 3)+3 2+4 0&2 5+3 4+4 5@3 1+4 0+5 3&3 ( 3)+4 2+5 0&2 5+4 4+5 5@4 1+5 0+6 3&4 ( 3)+5 2+6 0&2 5+5 4+6 5)]_(3 3) = [ 8(2+0+12& 6+6+0&10+12+20@3+0+15& 9+0+0&15+16+25@4+0+18& 12+10+0&20+20+30)] = [ 8(14&0&42@18& 1&56@22& 2&70)] Ex 3.2, 3 Compute the indicated products (v) [ 8( 2&1@ 3&2@ 1&1)] [ 8( 1&0&1@ 1&2&1)] [ 8( 2&1@ 3&2@ 1&1)]_(3 2) [ 8( 1&0&1@ 1&2&1)]_(2 3) = [ 8(2 1+1 ( 1)&2 0+1 2&2 1+1 1@3 1+2 ( 1)&3 0+2 2&3 1+2 1@ 1 1+(1) ( 1)& 1 0+1 2& 1 1+1 1)]_(3 3) = [ 8(2 1& 0+2&2+1@3 2&0+4&3+2@ 1 1&0+2& 1+1)] = [ 8(1&2&3@1&4&5@ 2&2&0)] Ex 3.2, 3 Compute the indicated products (vi) [ 8(3& 1&3@ 1&0&2)][ 8(2& 3@1&0@3&1)] [ 8(3& 1&3@ 1&0&2)]_"2 3" [ 8(2& 3@1&0@3&1)]_"3 2" = [ 8(3(2) 1(1)+3(3)&3( 3) 1(0)+3(1)@ 1(2)+0(1)+2(3)& 1( 3)+0(0)+2(1))]_(2 2) = [ 8(6 1+9& 9 0+3@ 2+0+6&3+0+2)] = [ 8(14& 6@4&5)]