Last updated at Dec. 8, 2016 by Teachoo

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

Chapter 3 Class 12 Matrices

Concept wise

- Formation and order of matrix
- Types of matrices
- Equal matrices
- Addition/ subtraction of matrices
- Statement questions - Addition/Subtraction of matrices
- Multiplication of matrices
- Statement questions - Multiplication of matrices
- Solving Equation
- Finding unknown - Element
- Finding unknown - Matrice
- Transpose of a matrix
- Symmetric and skew symmetric matrices
- Proof using property of transpose
- Inverse of matrix using elementary transformation
- Proof using mathematical induction

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.