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\begin{center}\large\bf
Linear Algebra 2270-2 \\
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Week 3
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The third week finishes the work from chapter 2. Here's the
list of problems, followed by problem notes and a few answers.

\begin{description}
\item[{\bf Section 2.1}.] Exercises 9, 10, 21, 29, 34

\item[{\bf Section 2.2}.] Exercises 5, 9, 12, 13, 32

\item[{\bf Section 2.3}.] Exercises 3, 13, 19, 25, 27, 28, 29

\end{description}


\subsection*{Problem Notes}

Resolution of issues for Strang's problems will appear here in response to communications. If there is a difficulty, like a missing definition or incomplete information, then please write email, call 581-6879, or visit JWB 113.

{\bf 1.2-13}.

{\bf 1.3-6}.

{\bf 1.3-10}.

\subsection*{Some Answers}

Only answers not in the back of the book appear below.

{\bf 2.1-9}. (a) $Ax = (18, 5, 0)$ and (b) $Ax = (3, 4, 5, 5)$.

{\bf 2.1-10}. Multiplying as linear combinations of the columns gives the same $Ax$. By rows or by
columns: 9 separate multiplications for 3 by 3.

{\bf 2.1-21}. $R=\frac{1}{\sqrt2}\left(\begin{array}{ll} 1 & -1 \\ 1 & 1 \end{array}\right)$. The entries are sines and cosines of $45$ degrees.

{\bf 2.1-29}.  $u_2 =\colvector{.7 \\ .3}$ and $u_3=\colvector{.65\\ .35}$. The components add to 1. They are always positive.
$u_7, v_7, w_7$ are all close to $\colvector{6.\\ .4}$. Their components still add to $1$.

{\bf 2.1-34}. 




{\bf 1.3-10}. 





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