If A₁, A₃, ..... A_{2n - 1} are n skew symmetric matrices of same order then B = Σlimits_{r = 1

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3 and 4 .Determinants and Matrices

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If $A_1, A_3, ..... A_{2n - 1}$ are $n$ skew symmetric matrices of same order then $B =$$\sum\limits_{r = 1}^n {(2r - 1){{({A_{2r - 1}})}^{2r - 1}}} $ will be

A

symmetric

B

skew symmetric

C

neither symmetric nor skew symmetric

D

data is adequate

Solution

$B = A_1 + 3A_3^3 + ….. (2n – 1) {({A_{2n – 1}})^{2n – 1}}$
$B^T = – [A_1 +3A_3^3 + ….. (2n – 1){({A_{2n – 1}})^{2n – 1}}$
$= – B$ so skew symmetric

Standard 12

Mathematics

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