Math 3592H Honors Mathematics I Fall Semester 2008

Assignment 9 - Due Thursday 11/6/2008

Read: Hubbard and Hubbard Section 2.1 and 2.2.

Exercises:
Hand in only the exercises which have stars by them.

Section 2.1: 2a*. All of questions 1 - 9 are instructive.
Section 2.2: 2e*, 3b*, 6*(for part b please identify completely the values of a for which there is a unique solution, no solution, and infinitely many solutions), 9*, 10*. In questions which ask you to solve a system of equations which has infinitely many solutions, find an expression for the general form of the solution. All of questions 1 - 10 are instructive.

Extra questions:
1. Express the vectors (1,0) and (0,1) as linear combinations of (1,2) and (2,3) by solving an appropriate system of equations for the coefficients of the combinations.

2. Express the vector (5,0,1,2) as a linear combinations of (1,2,1,0) and (2,-1,0,1).

3. In each of the following, determine whether or not the vector v is a 'linear combination' of the other vectors given, that is, whether v can be expressed as a sum of terms which are a scalar times a, b or c:
(a) v = 2i + 3j; a = 2i - j, b = 2i + j.
(b)* v = 2i + 3j + 4k; a = 2i - j, b = i + j + k, c = j - 2k.
(c) v = (3,-1,0,-1); a = (2,-1,3,2), b = (-1,1,1,-3), c = (1,1,9,-5).

4. Solve the systems