Check sibling questions

Example 17 - Calculate AC, BC, (A + B)C. Also, verify - Examples

Example 17 - Chapter 3 Class 12 Matrices - Part 2
Example 17 - Chapter 3 Class 12 Matrices - Part 3 Example 17 - Chapter 3 Class 12 Matrices - Part 4


Transcript

Example 17 If A = [■8(0&6&[email protected]−6&0&[email protected]&−8&0)], B = [■8(0&1&[email protected]&0&[email protected]&2&0)] , C = [█([email protected][email protected])] Calculate AC, BC and (A + B)C. Also, verify that (A + B)C = AC + BC Calculating AC AC = [■8(0&6&[email protected]−6&0&[email protected]&8&0)]_(3 × 3) [█([email protected][email protected])]_(3 × 1) = [█(0(2)+6(−2)+7(3)@−6(2)+0(−2)+8(3)@7(2)+8(−2)+0(3))]_(3 × 1) = [█(0−[email protected][email protected]+16+0)] = [█([email protected]@30)] Calculating BC BC = [■8(0&1&[email protected]&0&[email protected]&2&0)]_(3 × 3) [█([email protected][email protected])]_(3 × 1) = [█(0(2)+1(−2)+1(3)@1(2)+0(−2)+2(3)@1(2)+2(−2)+0(3))]_(3 × 1) = [█(0−[email protected][email protected]−4+0)] = [█([email protected]@−2)] Calculating AC + BC AC + BC =[█([email protected]@30)] + [█([email protected]@−2)] = [█([email protected][email protected]−2)] = [█([email protected]@28)] Calculating (A + B) C First calculating A + B A + B = [■8(0&6&[email protected]−6&0&[email protected]&−8&0)] +[■8(0&1&[email protected]&0&[email protected]&2&0)] = [■8(0+0&6+1&[email protected]−6+1&0+0&[email protected]+1&−8+2&0+0)] = [■8(0&7&[email protected]−5&0&[email protected]&−6&0)] Now, Calculating (A + B) C (A + B) C = [■8(0&7&[email protected]−5&0&[email protected]&−6&0)]_(3 × 3) [█([email protected][email protected])]_(3 × 1) = [█(0(2)+7(−2)+8(3)@−5(2)+0(−2)+10(3)@8(2)+(−6)(−2)+0(3))]_(3 × 1) = [█(0−[email protected][email protected]+12+0 )] = [█([email protected]@28)] = AC + BC ∴ 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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.