Misc 14 - If matrix A is both symmetric and skew symmetric - Symmetric and skew symmetric matrices

  1. Chapter 3 Class 12 Matrices
  2. Serial order wise

Transcript

Misc. 14 (Introduction) If the matrix A is both symmetric and skew symmetric, then A. A is a diagonal matrix B. A is a zero matrix C. A is a square matrix D. None of these Diagonal Matrix: Matrix with all non-diagonal elements zero. Eg: [ 8(1&0&0@0& 2&0@0&0&4)] , [ 8( 9&0@0&35)] Zero Matrix: Matrix with all elements zero Eg: [ 8(0&0&0@0&0&0@0&0&0)] , [ 8(0&0@0&0)] Square matrix Matrix with number of rows = Number of columns Eg: [ 8(6& 2&2@ 2&3& 1@2& 1&3)] , [ 8(1&6@5&7)] Misc. 14 If the matrix A is both symmetric and skew symmetric, then A. A is a diagonal matrix B. A is a zero matrix C. A is a square matrix D. None of these Since A is both symmetric and skew-symmetric matrix, A = A and A = A Comparing both equations A = A A + A = O 2A = O A = O Therefore, A is a zero matrix.

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.