Example 20 - Chapter 3 Class 12 Matrices
Last updated at April 16, 2024 by Teachoo
Examples
Example 2
Example 3 Important
Example 4
Example 5 Important
Example 6
Example 7
Example 8
Example 9
Example 10
Example 11 Important
Example 12
Example 13 Important
Example 14
Example 15
Example 16 Important
Example 17
Example 18 Important
Example 19
Example 20 Important You are here
Example 21
Example 22 Important
Example 23 Important
Example 24 Important
Example 25
Question 1 Deleted for CBSE Board 2025 Exams
Question 2 Important Deleted for CBSE Board 2025 Exams
Question 3 Important Deleted for CBSE Board 2025 Exams
Last updated at April 16, 2024 by Teachoo
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 Since 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 Since L.H.S = R.H.S Hence Proved.