# Example 20 - Chapter 3 Class 12 Matrices (Term 1)

Last updated at Jan. 17, 2020 by

Last updated at Jan. 17, 2020 by

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Example 20 If A = [■8(3&√3&2@4&2&0)] and B = [■8(2&−1&2@1&2&4)] Verify that (i) (A’)’ = A, A = [■8(3&√3&2@4&2&0)] A’ = [■8(3&√3&2@4&2&0)]^′= [■8(3&4@√3&2@2&0)] (A’)’ = [■8(3&4@√3&2@2&0)]^′= [■8(3&√3&2@4&2&0)] = A Thus (A’)’ = A Example 20 If A = [■8(3&√3&2@4&2&0)] and B = [■8(2&−1&2@1&2&4)] Verify that (i) (A’)’ = A, A = [■8(3&√3&2@4&2&0)] A’ = [■8(3&√3&2@4&2&0)]^′= [■8(3&4@√3&2@2&0)] (A’)’ = [■8(3&4@√3&2@2&0)]^′= [■8(3&√3&2@4&2&0)] = A Thus (A’)’ = A Example 20 If A = [■8(3&√3&2@4&2&0)] and B = [■8(2&−1&2@1&2&4)] Verify that (ii) (A + B)’ = A’ + B’, Solving L.H.S First finding (A + B) (A + B) = [■8(3&√3&2@4&2&0)] + [■8(2&−1&2@1&2&4)] = [■8(3+2 &√3+(−1)&2+2@4+1&2+2&0+4)] = [■8(5&√3−1&4@5&4&4)] Thus, (A + B)’ = [■8(5&5@√3−1&4@4&4)] Solving R.H.S A’ + B’ Finding A’ A = [■8(3&√3&2@4&2&0)] A’ = [■8(3&4@√3&2@2&0)] Also, B = [■8(2&−1&2@1&2&4)] B‘ = [■8(2&1@−1&2@2&4)] Now, A’ + B’ =[■8(3&4@√3&2@2&0)] +[■8(2&1@−1&2@2&4)] = [■8(3+2&4+1@√3+(−1)&2+2@2+0&0+4)] = [■8(5&5@√3−1&4@4&4)] = L.H.S Hence, L.H.S = R.H.S Hence Proved Example 20 If A = [■8(3&√3&2@4&2&0)] and B = [■8(2&−1&2@1&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&2@1&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&2@1&2&4)] B’ = [■8(2&1@−1&2@2&4)] kB’ = k[■8(2&1@−1&2@2&4)] = [■8(2𝑘&𝑘@−𝑘&2𝑘@2𝑘&4𝑘)] = L.H.S Hence, L.H.S = R.H.S Hence Proved.

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Example 20 Important You are here

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Example 22 Important

Example 23 Deleted for CBSE Board 2022 Exams

Example 24 Important Deleted for CBSE Board 2022 Exams

Example 25 Important Deleted for CBSE Board 2022 Exams

Example 26 Important

Example 27 Important

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Chapter 3 Class 12 Matrices (Term 1)

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.