Homework Assignment 4, due 10 March 2008

1. Exercise 2.2, page 89.

2. Exercise 2.30, page 112.

3. Exercise 2.36, page 120.

4. Exercise 2.37, page 120.

In exercise 2.37, remember that in a vector v, v_i represents the ith element of the vector, and in a matrix m, m_ij represents the element in the ith row and jth column of the matrix. Using the list ((1 2 3) (4 5 6)) to represent the matrix

 _     _
| 1 2 3 |
|_4 5 6_|

and (7 8 9) and (10 11 12) to represent vectors,
the dot product of (7 8 9) and (10 11 12) = 7*10 + 8*11 + 9*12 = 266.
matrix ((1 2 3) (4 5 6)) times vector (7 8 9) = ( 1*7+2*8+3*9 4*7+5*8+6*9 ) = (50 122).
matrix ((7 8) (9 10)) times ((1 2 3) (4 5 6)) = ((7*1+8*4 7*2+8*5 7*3+8*6) (9*1+10*4 9*2+10*5 9*3+10*6)) = ((39 54 69) (49 68 87))
transpose of ((1 2 3) (4 5 6)) = ((1 4) (2 5) (3 6)).