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Ex 3.3, 8 - 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, 8 For the matrix A = [■8(1&5@6&7)] , verify that (i) (A + A’) is a symmetric matrix A = [■8(1&5@6&7)] A’ = [■8(1&6@5&7)] A + A’ = [■8(1&5@6&7)] + [■8(1&6@5&7)] = [■8(𝟐&𝟏𝟏@𝟏𝟏&𝟏𝟒)] ∴ (A + A’)’ = [■8(𝟐&𝟏𝟏@𝟏𝟏&𝟏𝟒)] Since (A + A’)’ = A + A’ Hence, (A + A’) is a symmetric matrix. Ex 3.3, 8 For the matrix A = [■8(1&5@6&7)] , verify that (ii) (A – A’) is a skew symmetric matrix A = [■8(1&5@6&7)] A’ = [■8(1&6@5&7)] A – A’ = [■8(1&5@6&7)] − [■8(1&6@5&7)] = [■8(𝟎&−𝟏@𝟏&𝟎)] (A – A’)’ = [■8(0&1@−1&0)] = − [■8(0&−1@1&0)] = − (A – A’) Since, (A – A’)’ = – (A – A’) Hence, (A – A’) is a skew-symmetric matrix.
