Ex 3.2, 4 - Chapter 3 Class 12 Matrices

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Ex 3.2, 4 If A = [ 8(1&2& 3@5&0&2@1& 1&1)], B = [ 8(3& 1&2@4&2&5@2&0&3)] and , C = [ 8(4&1&2@0&3&2@1& 2&3)] then compute (A+B) and (B C) . Also, verify that A + (B C) = (A + B) C Calculating A + B A + B = [ 8(1&2& 3@5&0&2@1& 1&1)]+ [ 8(3& 1&2@4&2&5@2&0&3)] = [ 8(1+3&2 1& 3+2@5+4&0+2&2+5@1+2& 1+0&1+3)] = [ 8(4&1& 1@9&2&7@3& 1&4)] Calculating B C B C = [ 8(3& 1&2@4&2&5@2&0&3)] [ 8(4&1&2@0&3&2@1& 2&3)] = [ 8(3 4& 1 1&2 2@4 0&2 3&5 2@2 1&0 ( 2)&3 3)] = [ 8( 1& 2&0@4& 1&3@1&2&0)] We need to verify A + (B C) = (A + B) C Taking L.H.S A + (B C) = [ 8(1&2& 3@5&0&2@1& 1&1)]+ [ 8( 1& 2&0@4& 1&3@1&2&0)] = [ 8(1 1&2 2& 3+0@5+4&0 1&2+3@1+1& 1+2&1+0)] = [ 8(0&0& 3@9& 1&5@2&1&1)] Taking R.H.S (A + B) C = [ 8(4&1& 1@9&2&7@3& 1&4)] [ 8(4&1&2@0&3&2@1& 2&3)] = [ 8(4 4&1 1& 1 2@9 0&2 3&7 2@3 1& 1+2&4 3)] = [ 8(0&0& 3@9& 1&5@2&1&1)] = L.H.S Hence L.H.S = R.H.S Hence proved