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Ex 3.3, 6 - Verify that A’A = I if A = [cos a sin a - Transpose of a matrix

Ex 3.3, 6 - Chapter 3 Class 12 Matrices - Part 2

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Ex 3.3, 6 If (i) A = [ 8(cos &sin @ sin &cos )] , then verify that A A = I Taking L.H.S. A A Given A = [ 8(cos &sin @ sin &cos )] So, A = [ 8(cos & sin @sin &cos )] A A = [ 8(cos & sin @sin &cos )] [ 8(cos &sin @ sin &cos )] = [ 8(cos .cos + ( sin ) ( sin ) &cos .sin + ( sin )cos @sin . cos +cos ( sin ) &sin .sin +cos .cos )] = [ 8(cos2 +sin2 &sin cos sin cos @sin cos sin cos &sin2 +cos2 a)] = [ 8(cos2 +sin2 &0@0&sin2 +cos2 a)] Using sin2 + cos2 = 1 = [ 8(1&0@0&1)] = I = R.H.S Hence L.H.S = R.H.S Hence Proved

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