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{\Large 18.099 - 18.06CI.}
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{\large HW-2}
{Due on Monday, Feb 23 in class.
First draft due on Thursday, Feb 19}.
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\begin{enumerate}
\item{Find the dimension of the space of all homogeneous polynomials
of degree $p$ in $n$ variables. Prove your answer.
Make sure that it works in both cases $p \leq n$ and $p > n$, as
well as for the limit values $p=0$ and $n=1$.}
\item{Two linear spaces $L$ and $M$ over a field $F$ are isomorphic
if there exists a linear map $f : L \to M$ which is a set-theoretical
bijection (one-one and onto). Prove that two finite dimensional linear
spaces are isomorphic if and only if their dimensions coincide. }
\end{enumerate}
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