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\begin{center}\large\bf
Linear Algebra 2270-2 \\
\normalsize\rm
Due in Week 1
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For the first week, the plan is to submit one exercise, in order to get
started reading Lay's book. This first exercise requires methods from
sections 1.1, 1.2 and 1.3 of the textbook.

{\bf Exercise 1}.  {\large\em Write down three equations for $x, y, z$ so that
$x\vec{u} + y\vec{v}+z\vec{w} = \vec{b}$. Can you somehow
find the constants $x, y$ and $z$? }
$$
\vec{u}=\colvector{2 \\ -1 \\ 0}
,
\vec{v}=\colvector{-1 \\ 2 \\-1}
,
\vec{w}=\colvector{0 \\ -1 \\ 2}
,
\vec{b}=\colvector{1 \\ 0 \\ 0}
.
$$

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\subsection*{Opinion}
Gauss and Ramanujan were able to think of ideas unimaginable to their
contemporaries.
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%\includegraphics[scale=0.6]{gauss-karl-friedrich.jpeg}
\includegraphics[scale=1]{Carl-Friedrich-Gauss-1828.jpeg}
&
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 Karl Friedrich Gauss (1777-1855)      \\
Srinivasa Iyengar Ramanujan (1887-1920)
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&
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They were distinguished by their need to {\em create mathematics},
which they accomplished by having {\em ideas} and exploring them.

{\bf Gauss} is celebrated as the source from which algebraic and analytic
results flowed. His career spanned the years in which linear algebra
blossomed, especially determinants and matrices. Gauss elimination
is named after him, a topic which you will study in linear algebra. His thesis was the fundamental theorem of algebra.
His fundamental work in number theory was before age 24. In applied mathematics, he invented the method of least squares to solve
problems in orbital mechanics. Geodesics was next, then probabilistic methods. It is earnestly said that Gauss was probably the greatest mathematician of all time. He caused others to strive for concise proofs and to publish only complete results.

{\bf Ramanujan} is celebrated because he was a self-taught genius with humble
beginnings. If you work in isolation and are sorry for your background,
then read about Ramanujan and be inspired.

During 1903-1914, Ramanujan compiled 3,542 theorems in notebooks.
His work in number theory and analysis was halted in 1920, dead at age 32.
The results are now recognized as fundamental in general theories
developed since his death. He is credited for opening new areas of
research in mathematics, physics, computer science and statistics.


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