Ex 3.2, 4 - Chapter 3 Class 12 Matrices

Transcript

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