Check sibling questions

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

(a) 1 + ๐›ผ 2 + ๐›ฝ๐›พ = 0  (b) 1 − ๐›ผ 2 − ๐›ฝ๐›พ = 0

(c) 3 − ๐›ผ 2 − ๐›ฝ๐›พ = 0  (d) 3 + ๐›ผ 2 + ๐›ฝ๐›พ = 0

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Transcript

Question 40 Given that A = [โ– 8(๐›ผ&๐›ฝ@๐›พ&โˆ’๐›ผ )] and A2 = 3I, then : a) 1 + ๐›ผ2 + ๐›ฝ๐›พ = 0 b) 1 โˆ’ ๐›ผ2 โˆ’ ๐›ฝ๐›พ = 0 c) 3 โˆ’ ๐›ผ2 โˆ’ ๐›ฝ๐›พ = 0 d) 3 + ๐›ผ2 + ๐›ฝ๐›พ = 0 Given A2 = 3I [โ– 8(๐›ผ&๐›ฝ@๐›พ&โˆ’๐›ผ)] [โ– 8(๐›ผ&๐›ฝ@๐›พ&โˆ’๐›ผ)] = 3I [โ– 8(๐›ผ(๐›ผ)+๐›ฝ(๐›พ)&๐›ผ(๐›ฝ)+๐›ฝ(โˆ’๐›ผ)@๐›พ(๐›ผ)+(โˆ’๐›ผ)๐›พ&๐›พ(๐›ฝ)+(โˆ’๐›ผ)(โˆ’๐›ผ))] = 3 [โ– 8(1&0@0&1)] [โ– 8(๐œถ^๐Ÿ+๐œท๐œธ&๐ŸŽ@๐ŸŽ&๐œถ^๐Ÿ+๐œท๐œธ)] = [โ– 8(๐Ÿ‘&๐ŸŽ@๐ŸŽ&๐Ÿ‘)] Thus, ๐œถ^๐Ÿโคถ7+๐œท๐œธ = 3 0 = 3 โˆ’ ๐›ผ^2โˆ’๐›ฝ๐›พ 3 โˆ’ ๐›ผ2 โˆ’ ๐›ฝ๐›พ = 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.