જો શ્રેણિક A = {left[ {{a_{ij}}} right]_{3 × 3}} , B = {left[ {{b_{ij}}} rig

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3 and 4 .Determinants and Matrices

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જો શ્રેણિક $A = {\left[ {{a_{ij}}} \right]_{3 \times 3}} , B = {\left[ {{b_{ij}}} \right]_{3 \times 3}}$ , કે જ્યાં $a_{ij} + a_{ji} = 0$ અને $b_{ij} -b_{ji} = 0\, \forall\, i , j$ હોય તો $A^4B^3$ એ . . . શ્રેણિક હોય.

A

અસમાન્ય

B

શૂન્ય શ્રેણિક

C

સંમિત

D

વિસંમિત

Solution

Hence $a_{i j}=-a_{j j} \Rightarrow A^{T}=-A$ and $B^{T}=B$

and $\mathrm{A}, \mathrm{B}$ are $3 \times 3$ matrices,

Hence $|\mathrm{A}|=0 \Rightarrow\left|\mathrm{A}^{4} \mathrm{B}^{3}\right|=0 \Rightarrow \mathrm{A}^{4} \mathrm{B}^{3}$ is singular

Standard 12

Mathematics

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normal