Addition/ subtraction of matrices

Chapter 3 Class 12 Matrices
Concept wise

### Transcript

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 Solving 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)] Solving 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

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#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.