Ex 3.3, 6 - Chapter 3 Class 12 Matrices

Transcript

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