Given that A = [8(α β γ -α )] and A 2 = 3I, then :

(a) 1 + 𝛼 2 + 𝛽𝛾 = 0  (b) 1 − 𝛼 2 − 𝛽𝛾 = 0

(c) 3 − 𝛼 2 − 𝛽𝛾 = 0  (d) 3 + 𝛼 2 + 𝛽𝛾 = 0

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Transcript

Question 40 Given that A = [■8(𝛼&𝛽@𝛾&−𝛼 )] and A2 = 3I, then : a) 1 + 𝛼2 + 𝛽𝛾 = 0 b) 1 − 𝛼2 − 𝛽𝛾 = 0 c) 3 − 𝛼2 − 𝛽𝛾 = 0 d) 3 + 𝛼2 + 𝛽𝛾 = 0 Given A2 = 3I [■8(𝛼&𝛽@𝛾&−𝛼)] [■8(𝛼&𝛽@𝛾&−𝛼)] = 3I [■8(𝛼(𝛼)+𝛽(𝛾)&𝛼(𝛽)+𝛽(−𝛼)@𝛾(𝛼)+(−𝛼)𝛾&𝛾(𝛽)+(−𝛼)(−𝛼))] = 3 [■8(1&0@0&1)] [■8(𝜶^𝟐+𝜷𝜸&𝟎@𝟎&𝜶^𝟐+𝜷𝜸)] = [■8(𝟑&𝟎@𝟎&𝟑)] Thus, 𝜶^𝟐⤶7+𝜷𝜸 = 3 0 = 3 − 𝛼^2−𝛽𝛾 3 − 𝛼2 − 𝛽𝛾 = 0 So, the correct answer is (C)

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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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.