Misc. 14 - Chapter 3 Class 12 Matrices

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. So, B is the correct answer