First slide

Transpose of matrix

Question

If A₁, A₃, . . ., A_2n-1 are n skew-symmetric matrices of same order, then $B = \sum_{r = 1}^{n} (2 r - 1) {(A_{2 r - 1})}^{2 r - 1}$ will be

Moderate

A

symmetric
B

skew-symmetric
C

neither symmetric nor skew-symmetric
D

datanot adequate

Solution

$\begin{matrix} B = A_{1} + 3 A_{3}^{3} + \dots + (2 n - 1) {(A_{2 n - 1})}^{2 n - 1} \\ B^{T} = - [A_{1} + 3 A_{3}^{3} + \dots + (2 n - 1) {(A_{2 r - 1})}^{2 r - 1}] \\ = - B \end{matrix}$
Hence, B is skew-symmetric.

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