Symmetric and skew symmetric matrices

Chapter 3 Class 12 Matrices
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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 