Symmetric and skew symmetric matrices

Chapter 3 Class 12 Matrices
Concept wise

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### 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&[email protected]&−2&[email protected]&0&4)] , [■8(−9&[email protected]&35)] Zero Matrix: Matrix with all elements zero Eg: [■8(0&0&[email protected]&0&[email protected]&0&0)] , [■8(0&[email protected]&0)] Square matrix Matrix with number of rows = Number of columns Eg: [■8(6&−2&2@−2&3&−[email protected]&−1&3)] , [■8(1&[email protected]&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. So, B is the correct answer

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.