3 and 4 .Determinants and Matrices
easy

જો $ A$  એ ચોરસ શ્રેણિક છે કે જેથી ${a_{ij}} = {i^2} - {j^2}$, તો  $ A $ એ . . . . શ્રેણિક થાય.

A

શૂન્ય

B

એકમ

C

સંમિત

D

વિસંમિત

Solution

(d)${a_{ji}} = {i^2} – {j^2}$ is a square matrix. For a skew symmetric matrix ${a_{ji}} = -{a_{ji}}$

$\Rightarrow$ ${a_{ij}} = {i^2} – {j^2}$ and ${a_{ji}} = {j^2} – {i^2}$

$\Rightarrow$ ${a_{ij}} + {a_{ji}} = 0 $

$\Rightarrow \,{a_{ij}} =  – {a_{ji}}$

Hence, $ {a_{ji}}$ is a skew symmetric matrix.

Standard 12
Mathematics

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