CE_Feb2.tex

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\begin{document}
\begin{center}
\Large
\rm{Math 221}
\\
\rm{Class Exercises:  Feb. 2}
\\
\end{center}
\vspace{0.2in}
\fboxsep0.5cm



\begin{displaymath}
x_1 = \left[ \begin{array}{r} 1 \\ 0 \\ 2 \end{array}\right]
\quad\quad
x_2 = \left[ \begin{array}{r} 8 \\ 2 \\ -1 \end{array}\right]
\quad\quad
x_3 = \left[ \begin{array}{r} 4 \\ 2 \\ -9 \end{array}\right]
\end{displaymath}

\vspace{0.5in}

Find a linear combination of $x_1$, $x_2$, and $x_3$ with the last entry in the vector equal to $2$.

\vspace{0.1in}

\begin{displaymath}
c_1\left[ \begin{array}{r} 1 \\ 0 \\ 2 \end{array}\right]
+
c_2\left[ \begin{array}{r} 8 \\ 2 \\ -1 \end{array}\right]
+
c_3\left[ \begin{array}{r} 4 \\ 2 \\ -9 \end{array}\right]=
\left[ \begin{array}{r} * \\ * \\ 2 \end{array}\right]
\end{displaymath}

\vspace{1.5in}

Can you find a linear combination $x_1$, $x_2$, and $x_3$ such that all the entries are equal to $2$?

\vspace{2.5in}

Is the vector $b$ in the subspace spanned by $v_1$ and $v_2$?

\begin{displaymath}
v_1 = \left[ \begin{array}{r} 5 \\ 2 \\ -1 \end{array}\right]
\quad\quad
v_2 = \left[ \begin{array}{r} 1 \\ 1 \\ -2 \end{array}\right]
\quad\quad
b = \left[ \begin{array}{r} 0 \\ 0 \\ 1 \end{array}\right]
\end{displaymath}

\vspace{4in}


\end{document}