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Ex 3.3, 6 (i) - Chapter 3 Class 12 Matrices
Last updated at May 29, 2023 by Teachoo
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
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 &[email protected]&sin2 +cos2 a)] Using sin2 + cos2 = 1 = [ 8(1&[email protected]&1)] = I = R.H.S Hence L.H.S = R.H.S Hence Proved
