1. In 1.1 #19, the augmented matrix was Matrix([[1,h,4],[3,6,8]])
Note this is Maple notation - each row of the matrix is in brackets.
Eliminate the number 3 using Gaussian elimination. Which of the following are true:
a) The Gaussian reduced matrix is Matrix([[1,h,4],[0,6-3h,-4]])
b) The system is consistent for all h
c) The system is inconsistent for h=2
d) a) and b)
e) a) and c)

2. What is the solution to the system of equations represented with this reduced augmented matrix?
1 0 0 2
0 1 0 3
0 0 1 4

a) (2,3,4)
b) (1,1,1)
c) There are an infinite number of solutions
d) There are no solutions
e) We can't tell without having the system of equations

3. If a linear system with 3 equations and 3 variables is inconsistent then we must have
a) at least 2 of the planes parallel
b) a missing pivot for some x_i
c) some row in the reduced augmented matrix is [0 0 0 nonzero]
d) more than one of the above
e) none of the above

4. How many solutions to a linear system of equations are possible?
a) 0 or 1
b) 0, 1, or 2
c) 0, 1, 2 or infinite
d) 0, 1, infinite
e) any number of solutions is possible
5. According to the language of linear algebra, this picture a)lies inside of R2, the x-y plane.
b)shows 3 linear equations that have 3 lines as the solutions
c)shows that 3 non-parallel planes do not have to have any points in common
d)more than one of the above choices are possible

6. How can we geometrically represent the parametric equations (2t, -t + 1, t)?
a) A line in R2
b) A line in R3
c) A plane in R3
d) A volume in R3

7. For a system of three linear equations in three variables, which of the following scenarios would always guarantee an infinite number of solutions?

a) At least two of the equations represent the same plane.
b) The three planes intersect along a line.
c) The planes represented are parallel.
d) More than one of the above choices are possible.
e) None of the above

8. Use Gaussian on the following augmented matrix:
1 1 0 2
2 1 3 3
2 2 h 4
Which of the following are true?
a) it takes at least 3 elementary row operations to get to Gaussian here
b) from Gaussian we can see that we have full pivots for all h
c) from Gaussian we can see that some h give us no solutions
d) more than one of the above is true
e) none of the above

9. For full credit, which of the following are true regarding graded problem sets:
a) I am only allowed to use the book, my group members, the math lab and Dr. Sarah for help on the problem set.
b) I can use any source for help, but the work and explanations must be distinguished as originating from my own group and I must acknowledge any help outside the group or Dr. Sarah, like "the idea for problem 1 came from discussions with johnny or this website..."

10. For full credit, which of the following are true regarding graded problem sets
a) I must print out all work, including Maple ReducedRowEchelonForm commands and output
b) I must annotate/explain my methods and reasoning with handwritten comments and/or typed comments.
c) both a) and b)
d) neither a) nor b)

Solutions:
1. e)
2. a)
3. d) [b) and c)]
4. d)
5. c)
6. b)
7. b)
8. e)
9. b)
10. c)