LINEAR ALGEBRA (Math 211)
HW #5 (Due Mon. Oct. 2 )

Compute the following determinants:

1. $\left\vert\begin{array}{rr}
-1&4\\
-5&2
\end{array}\right\vert$         2. $\left\vert\begin{array}{rr}
\cos\alpha & \sin\alpha\\
-\sin\alpha& \cos\alpha
\end{array}\right\vert$         3. $\left\vert\begin{array}{rr}
1&1\\
x&y
\end{array}\right\vert$         4. $\left\vert\begin{array}{rrr}
1&2&3\\
4&5&6\\
7&8&9
\end{array}\right\vert$         5. $\left\vert\begin{array}{rrr}
1&0&2\\
0&2&0\\
2&0&3
\end{array}\right\vert$


6. $\left\vert\begin{array}{rrr}
2&0&1\\
1&2&1\\
0&1&2
\end{array}\right\vert$         7. $\left\vert\begin{array}{rrr}
9&10&11\\
1&1&1\\
2&3&4
\end{array}\right\vert$         8. $\left\vert\begin{array}{rrr}
-1&5&2\\
0&7&0\\
1&2&0
\end{array}\right\vert$



9. $\textstyle \parbox{12cm}{Compute the following Vandermonde's determinant.
Factorize the answer.}$        $\textstyle \parbox{4cm}{
$\left\vert\begin{array}{rrr}
1&10&1\\
x&y&z\\
x^2&y^2&z^2
\end{array}\right\vert$}$



10. $\textstyle \parbox{10cm}{Find all values of $\lambda$\ for which the
following
determinant will equal $0$.}$        $\textstyle \parbox{4cm}{
$\left\vert\begin{array}{rr}
2-\lambda&4\\
3&3-\lambda
\end{array}\right\vert$}$