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**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