Home
Class 11
MATHS
For any nxxn matrix A, prove that A can ...

For any `nxxn` matrix A, prove that A can be uniquely expressed as a sum of a symmetric matrix and a skew symmetric matrix.

Text Solution

Verified by Experts

The correct Answer is:
`1/2(A-A^(T))`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    AAKASH SERIES|Exercise ADDITIONAL SOLVED EXAMPLES|9 Videos

  • MATRICES

    AAKASH SERIES|Exercise Exercise - 3.1 (Very short answer questions)|20 Videos

  • MATHEMATICAL INDUCTION

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE-I) LEVEL-I (Principle of Mathematical Induction) (Straight Objective Type Questions)|55 Videos

  • MAXIMA & MINIMA

    AAKASH SERIES|Exercise EXERCISE-III|35 Videos

Similar Questions

Explore conceptually related problems

Define Trace of a matrix and skew symmetric matrix.

A is a symmetric matrix or skew symmetric matrix. Then A^(2) is

If a matrix A is both symmetric and skew symmetric then A is

Express A=[(2,0,-3),(4,3,1),(-5,7,2)] as a sum of a symmetric and a skew symmetric matrix

If A and B are symmetric matrices, prove that AB-BA is a skew symmetric matrix.

The inverse of a skew symmetric matrix of odd order is

For any square matrix A, show that AA' is symmetric.

For any square matrix A, show that AA' is symmetric.