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TIFR-2012-Maths-B: 18

soujanyareddy13 asked in TIFR Aug 30, 2020 edited Oct 19, 2020 by soujanyareddy13

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True/False Question:

Any $3\times3$ and $5\times5$ skew-symmetric matrices have always zero determinants.

tifrmaths2012

soujanyareddy13 asked in TIFR Aug 30, 2020 edited Oct 19, 2020 by soujanyareddy13

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TIFR-2012-Maths-B: 11
True/False Question: The automorphism group $Aut\left ( \mathbb{Z}/2\times \mathbb{Z}/2 \right )$ is abelian.

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TIFR-2012-Maths-B: 12
True/False Question: Let $V$ be the vector space of consisting polynomials of $\mathbb{R}\left [ t \right ]$ of deg$\leq 2$. The map $T:V\rightarrow V$ sending $f\left ( t \right )$ to $f\left ( t \right )+{f}'\left ( t \right )$ is invertible.

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TIFR-2012-Maths-B: 13
True/False Question: The polynomials $\left ( t-1 \right )\left ( t-2 \right ),\left ( t-2 \right )\left ( t-3 \right ),\left ( t-3 \right )\left ( t-4 \right ),\left ( t-4 \right )\left ( t-6 \right )\in \mathbb{R}\left [ t \right ]$ are linearly independent.

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soujanyareddy13 asked in TIFR Aug 30, 2020

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TIFR-2012-Maths-B: 14
True/False Question: $A\in M_{2}\left ( \mathbb{C} \right )$and $A$ is nilpotent then $A^{2}=0$.

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tifrmaths2012

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