Tentative list.

*: Recommended question. Not required if you know you can do it.

#: Make a graph.

$^0$ $z$-component is 2$t \hat k$

$^1$ Use determinants.

$^2$ Answer for a may be wrong, depending on book.

$^3$ Use GE. Do not take any determinants

$^{4a}$ Use minors.

$^{4b}$ Use Gaussian elimination.

$^5$ Orthonormal matrix.

$^6$ The value of $b_{21}$ in the first column is 2, not 4. Be careful not to make errors in the determinant. Since $u$ and $v$ are nonunique, find those that result from Gram-Schmidt orthogonalization of the basis of the null space.

$^7$ 21, not 20.

$^8$ answer for b may be wrong.