Check sibling questions

Misc 6 - Find x, y, z if the matrix A satisfies A'A = I - Miscellaneou

Misc. 6 - Chapter 3 Class 12 Matrices - Part 2
Misc. 6 - Chapter 3 Class 12 Matrices - Part 3


Transcript

Misc 6 Find the values of x, y, z if the matrix A = [■8(0&2𝑩&𝑧@đ‘„&𝑩&−𝑧@đ‘„&−𝑩&𝑧)] satisfy the equation Aâ€ČA = I. Given, A = [■8(0&2𝑩&𝑧@đ‘„&𝑩&−𝑧@đ‘„&−𝑩&𝑧)] A’ = [■8(0&đ‘„&đ‘„@2𝑩&𝑩&−𝑩@𝑧&−𝑧&𝑧)] I = [■8(1&0&0@0&1&0@0&0&1)] Now, A’A = I Putting values [■8(0&đ‘„&đ‘„@2𝑩&𝑩&−𝑩@𝑧&−𝑧&𝑧)][■8(0&2𝑩&𝑧@đ‘„&𝑩&−𝑧@đ‘„&−𝑩&𝑧)] = [■8(1&0&0@0&1&0@0&0&1)] [■8(0(0)+đ‘„(đ‘„)+đ‘„(đ‘„)&0(2𝑩)+đ‘„(𝑩)+đ‘„(−𝑩)&0(𝑧)+đ‘„(−𝑧)+đ‘„(𝑧)@2𝑩(0)+𝑩(đ‘„)−𝑩(đ‘„)&2𝑩(2𝑩)+𝑩(𝑩)−𝑩(−𝑩)&2𝑩(𝑧)+𝑩(−𝑧)−𝑩(𝑧)@𝑧(0)−𝑧(đ‘„)+𝑧(đ‘„)&𝑧(2𝑩)−𝑧(𝑩)+𝑧(−𝑩)&𝑧(𝑧)−𝑧(−𝑧)+𝑧(𝑧))] = [■8(1&0&0@0&1&0@0&0&1)] [■8(0+đ‘„^2+đ‘„^2&0+đ‘„đ‘Šâˆ’đ‘„đ‘Š&0âˆ’đ‘„đ‘§+đ‘„đ‘§@0+đ‘„đ‘Šâˆ’đ‘„đ‘Š&4𝑩^2+𝑩^2+𝑩^2&2𝑧𝑩−𝑧𝑩−𝑧𝑩@0âˆ’đ‘„đ‘§+đ‘„đ‘§&2𝑧𝑩−𝑧𝑩−𝑧𝑩&𝑧^2+𝑧^2+𝑧^2 )]= [■8(1&0&0@0&1&0@0&0&1)] [■8(2đ‘„^2&0&0@0&6𝑩^2&0@0&0&3𝑧^2 )]= [■8(1&0&0@0&1&0@0&0&1)] Since matrices are equal, corresponding elements are equal Thus, x = ± 1/√2 , y = ± 1/√6 , z = ± 1/√3 2x2 = 1 x2 = 1/2 x = ±√(1/2) x = ± 𝟏/√𝟐 6y2 = 1 y2 = 1/6 y = ±√(1/6) y = ± 𝟏/√𝟔 3z2 = 1 z2 = 1/3 z = ±√(1/3) z = ± 𝟏/√𝟑

Davneet Singh's photo - Teacher, Engineer, Marketer

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.