TYPES, PROPERTIES, SYMMETRIC & SKEW SYMMETRIC MATRIX

Symmetric & Skew metric matrix

STATEMENT -1 All positive odd integral powers of a skew - symmetric matrix are symmetric. STATEMENT-2 : All positive even integral powers of a skew - symmetric matrix are symmetric. STATEMENT-3 If A is a skew - symmetric matrix of even order then |A| is perfect square

Orthogonal Matrix ||Symmetric Matrix || Skew Symmetric Matrix

If A and B are symmetric matrices of same order, then STATEMENT-1: A+B is skew - symmetric matrix. STATEMENT -2 : AB-BA is skew - symmetric matrix. STATEMENT-3 A-B is skew - symmetric matrix .

Transpose Of Matrix|Examples|Symmetric Matrix|Skew - Symmetric Matrix|Important Theorem|OMR|Quiz|Summary

Let A be a square matrix and k be a scalar. Prove that (i) If A is symmetric, then kA is symmetric. (ii) If A is skew-symmetric, then kA is skew-symmetric.

If Ais symmetric and B is skew-symmetric matrix, then which of the following is/are CORRECT ?

Properties OF determinant || Some Special Determinants || Cyclic || Symmetric & Skew symmetric determinant

For the matrix A=[[1, 5],[ 6, 7]] , verify that.(i) (A+A^(prime)) is a symmetric matrix(ii) (A-A^(prime)) is a skew symmetric matrix

for the matrix A=[{:(1,5),(6,7):}], verify that : (I) (A+A') is a symmetric matrix. (ii) (A-A') is a skew symmetric matrix.