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TIFR-2012-Maths-B: 14
soujanyareddy13
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True/False Question:
$A\in M_{2}\left ( \mathbb{C} \right )$and $A$ is nilpotent then $A^{2}=0$.
tifrmaths2012
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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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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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True/False Question: Let $P$ be an $n \times n $ matrix whose row sums equal $1$. Then for any positive integer $m$ the row sums of the matrix $p^{m}$ equal $1$.
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