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Ex 3.3, 9 - Chapter 3 Class 12 Matrices
Last updated at Dec. 16, 2024 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, 9 Find 1/2 (A + A’)and 1/2 (A – A’) , when A = [■8(0&a&b@−a&0&c@−b&−c&0)] A = [■8(0&a&b@−a&0&c@−b&−c&0)] A‘ = [■8(0&−a&−b@a&0&−c@b&c&0)] 1/2 (A + A’) = 1/2 ([■8(0&a&b@−a&0&c@−b&−c&0)]"+" [■8(0&−a&−b@a&0&−c@b&c&0)]) = 1/2 [■8(0&0&0@0&0&0@0&0&0)] = [■8(𝟎&𝟎&𝟎@𝟎&𝟎&𝟎@𝟎&𝟎&𝟎)] 𝟏/𝟐 (A − A’) = 1/2 ([■8(0&𝑎&𝑏@−𝑎&0&𝑐@−𝑏&−𝑐&0)]−[■8(0&−𝑎&−𝑏@𝑎&0&−𝑐@𝑏&𝑐&0)]) = 𝟏/𝟐 [■8(𝟎&𝟐𝒂&𝟐𝒃@−𝟐𝒂&𝟎&𝟐𝒄@−𝟐𝒃&−𝟐𝒄&𝟎)] = [■8(1/2×0&1/2×2𝑎&1/2×2𝑏@1/2×−2𝑎&1/2×0&1/2×2𝑐@1/2×−2𝑏&1/2×−2𝑐&1/2×0)] = [■8(𝟎&𝒂&𝒃@−𝒂&𝟎&𝒄@−𝒃&−𝒄&𝟎)]
