CPS 304 Homework 1 Due: Jan. 30

1)
Suppose you have the following vectors/matrices with indicated dimensions:

What are the resulting dimensions of the following calculations:

If you cannot perform an operation, state why not. Also, if the result is a vector, state whether it is a row vector or column vector.

2)
Given the vectors

compute the following:
3)
Given the quantities

compute the following: If a quantity cannot be computed, state the reason why.
4)
For and as defined above, compute
5)
Prove that

is a norm (i.e., show that this definition satisfies conditions i) - iv) in Section 4 of the Linear Algebra Handout).
6)
Prove that

7)
Prove that

8)
(Extra Credit) Prove that

is not a norm (HINT: Find 2 matrices that violate condition v) in Section 4).

2015-01-25