Misc. 14 - Chapter 3 Class 12 Matrices (Term 1)

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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. So, B is the correct answer