- Compute the determinant of $\begin{bmatrix}0&2&-1\\4&5&-2\\1&3&1\end{bmatrix}$.
- Find the area of a triangle with vertices $(0,0),(a,b), (c,d)$.
- Solve the system of equations $x+2y-3z=2$, $y-2z=1$. You might want to start by letting $z=t$, and then solving for $y$ and then $x$ in terms of $t$.
- Suppose we know $x=at+b$, $y=ct+d$, and $z=et+f$. Write this in the form $\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}?\\?\\?\end{bmatrix}t+\begin{bmatrix}?\\?\\?\end{bmatrix}$.
- The volume of a cylinder is $V=\pi r^2 h$. Compute $dV$ in terms of $r, h, dr, dh$. Then write your answer as the matrix product $$ dV = \begin{bmatrix}?&?\end{bmatrix}\begin{bmatrix}dr\\dh\end{bmatrix}.$$
- Compute $\int \arcsin x dx$.
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