Pt1420 Unit 3 Assignment

ISyE 3133B Spring 2011

Assignment 1
Assigned on Friday 1/14/2011
Due by 10:00am on Wednesday 1/19/2011

1. Expand the following summations:
(For example, the answer to part (a) is x1 + x2 + x3 .)
(a)
(c)

3 i=1 xi
3
t t=1 2 w2t

(b)
(d)

3 i=1 5 n=3 4 j=2 (xi + yij ) n+3 m=n+1 xn ym






2
3
2. Consider the following two vectors: x =  1  and y =  1 .
4
2
(a) What is dimension of x and y?
(b) Compute x + 2y.
(c) Compute ||x − y||.
(d) Compute xT (x + y).
(e) Compute x2 y1 .
3. Consider the following system of equations with unknowns x1 , x2 and x3 : x1 = 3x2 − 2x1 + 4 − x3 x2 + 2x1 = 4
4x1 + x2 − 3x3 = 6 − x2
Express this system in matrix vector notation in the form of
Ax = b
where