Learn All Concepts of Chapter 3 Class 12 Matrices - FREE. Check - Matrices Class 12 - Full video


Last updated at Jan. 17, 2020 by Teachoo
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Misc 6 Find the values of x, y, z if the matrix A = [โ 8(0&2๐ฆ&๐ง@๐ฅ&๐ฆ&โ๐ง@๐ฅ&โ๐ฆ&๐ง)] satisfy the equation AโฒA = I. Given, A = [โ 8(0&2๐ฆ&๐ง@๐ฅ&๐ฆ&โ๐ง@๐ฅ&โ๐ฆ&๐ง)] Aโ = [โ 8(0&๐ฅ&๐ฅ@2๐ฆ&๐ฆ&โ๐ฆ@๐ง&โ๐ง&๐ง)] I = [โ 8(1&0&0@0&1&0@0&0&1)] Now, AโA = I Putting values [โ 8(0&๐ฅ&๐ฅ@2๐ฆ&๐ฆ&โ๐ฆ@๐ง&โ๐ง&๐ง)][โ 8(0&2๐ฆ&๐ง@๐ฅ&๐ฆ&โ๐ง@๐ฅ&โ๐ฆ&๐ง)] = [โ 8(1&0&0@0&1&0@0&0&1)] [โ 8(0(0)+๐ฅ(๐ฅ)+๐ฅ(๐ฅ)&0(2๐ฆ)+๐ฅ(๐ฆ)+๐ฅ(โ๐ฆ)&0(๐ง)+๐ฅ(โ๐ง)+๐ฅ(๐ง)@2๐ฆ(0)+๐ฆ(๐ฅ)โ๐ฆ(๐ฅ)&2๐ฆ(2๐ฆ)+๐ฆ(๐ฆ)โ๐ฆ(โ๐ฆ)&2๐ฆ(๐ง)+๐ฆ(โ๐ง)โ๐ฆ(๐ง)@๐ง(0)โ๐ง(๐ฅ)+๐ง(๐ฅ)&๐ง(2๐ฆ)โ๐ง(๐ฆ)+๐ง(โ๐ฆ)&๐ง(๐ง)โ๐ง(โ๐ง)+๐ง(๐ง))] = [โ 8(1&0&0@0&1&0@0&0&1)] [โ 8(0+๐ฅ^2+๐ฅ^2&0+๐ฅ๐ฆโ๐ฅ๐ฆ&0โ๐ฅ๐ง+๐ฅ๐ง@0+๐ฅ๐ฆโ๐ฅ๐ฆ&4๐ฆ^2+๐ฆ^2+๐ฆ^2&2๐ง๐ฆโ๐ง๐ฆโ๐ง๐ฆ@0โ๐ฅ๐ง+๐ฅ๐ง&2๐ง๐ฆโ๐ง๐ฆโ๐ง๐ฆ&๐ง^2+๐ง^2+๐ง^2 )]= [โ 8(1&0&0@0&1&0@0&0&1)] [โ 8(2๐ฅ^2&0&0@0&6๐ฆ^2&0@0&0&3๐ง^2 )]= [โ 8(1&0&0@0&1&0@0&0&1)] Since matrices are equal, corresponding elements are equal Thus, x = ยฑ 1/โ2 , y = ยฑ 1/โ6 , z = ยฑ 1/โ3 2x2 = 1 x2 = 1/2 x = ยฑโ(1/2) x = ยฑ ๐/โ๐ 6y2 = 1 y2 = 1/6 y = ยฑโ(1/6) y = ยฑ ๐/โ๐ 3z2 = 1 z2 = 1/3 z = ยฑโ(1/3) z = ยฑ ๐/โ๐
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