Check sibling questions

Example 20 - Verify (i) (A')' = A (ii) (A + B)' = A' + B'

Example 20 - Chapter 3 Class 12 Matrices - Part 2
Example 20 - Chapter 3 Class 12 Matrices - Part 3 Example 20 - Chapter 3 Class 12 Matrices - Part 4 Example 20 - Chapter 3 Class 12 Matrices - Part 5 Example 20 - Chapter 3 Class 12 Matrices - Part 6


Transcript

Example 20 If A = [■8(3&√3&[email protected]&2&0)] and B = [■8(2&−1&[email protected]&2&4)] Verify that (i) (A’)’ = A, A = [■8(3&√3&[email protected]&2&0)] A’ = [■8(3&√3&[email protected]&2&0)]^′= [■8(3&[email protected]√3&[email protected]&0)] (A’)’ = [■8(3&[email protected]√3&[email protected]&0)]^′= [■8(3&√3&[email protected]&2&0)] = A Thus (A’)’ = A Example 20 If A = [■8(3&√3&[email protected]&2&0)] and B = [■8(2&−1&[email protected]&2&4)] Verify that (i) (A’)’ = A, A = [■8(3&√3&[email protected]&2&0)] A’ = [■8(3&√3&[email protected]&2&0)]^′= [■8(3&[email protected]√3&[email protected]&0)] (A’)’ = [■8(3&[email protected]√3&[email protected]&0)]^′= [■8(3&√3&[email protected]&2&0)] = A Thus (A’)’ = A Example 20 If A = [■8(3&√3&[email protected]&2&0)] and B = [■8(2&−1&[email protected]&2&4)] Verify that (ii) (A + B)’ = A’ + B’, Solving L.H.S First finding (A + B) (A + B) = [■8(3&√3&[email protected]&2&0)] + [■8(2&−1&[email protected]&2&4)] = [■8(3+2 &√3+(−1)&[email protected]+1&2+2&0+4)] = [■8(5&√3−1&[email protected]&4&4)] Thus, (A + B)’ = [■8(5&[email protected]√3−1&[email protected]&4)] Solving R.H.S A’ + B’ Finding A’ A = [■8(3&√3&[email protected]&2&0)] A’ = [■8(3&[email protected]√3&[email protected]&0)] Also, B = [■8(2&−1&[email protected]&2&4)] B‘ = [■8(2&[email protected]−1&[email protected]&4)] Now, A’ + B’ =[■8(3&[email protected]√3&[email protected]&0)] +[■8(2&[email protected]−1&[email protected]&4)] = [■8(3+2&[email protected]√3+(−1)&[email protected]+0&0+4)] = [■8(5&[email protected]√3−1&[email protected]&4)] = L.H.S Hence, L.H.S = R.H.S Hence Proved Example 20 If A = [■8(3&√3&[email protected]&2&0)] and B = [■8(2&−1&[email protected]&2&4)] .Verify that (iii) (kB)’ = kB’, where k is any constant. Solving L.H.S (kB)’ Finding kB first kB = k [■8(2&−1&[email protected]&2&4)] = [■8(2𝑘&−𝑘&2𝑘@𝑘&2𝑘&4𝑘)] (kB)’ = [■8(2𝑘&𝑘@−𝑘&2𝑘@2𝑘&4𝑘)] Solving R.H.S kB’ Finding B’ first B = [■8(2&−1&[email protected]&2&4)] B’ = [■8(2&[email protected]−1&[email protected]&4)] kB’ = k[■8(2&[email protected]−1&[email protected]&4)] = [■8(2𝑘&𝑘@−𝑘&2𝑘@2𝑘&4𝑘)] = 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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.