1. In the homework due today, did you use something similar to the following critical analysis/reasoning?
Multiply both sides of an equation by the inverse of a matrix
Associativity to move the parenthesis
Cancel A by using MatrixInverse(A)
Reduce Identity

a) Yes and I used it more than once
b) Yes and I used it once
c) No, although I used a similar reasoning
d) No, I didn't use anything like it
e) What homework?

2. If A is an invertible nxn matrix, and x and b are nx1 vectors, then the matrix-vector equation Ax = b has a unique solution.
a) True
b) Always false
c) Sometimes true and sometimes false

3. If Ax = 0 vector, then is C(Ax) = 0C?
a) Yes and I have a good reason why.
b) Yes but I am unsure of why.
c) No butI am unsure of why not.
d) No andI have a good reason why not.

4. If A is an invertible nxn matrix, where n>1, and x and b are 1xn vectors, then the matrix-vector equation Ax = b has a unique solution.
a) True
b) Always false
c) Sometimes true and sometimes false

5. If A is invertible and AB=AC then B=C sometimes but not always.
a) True and I can explain why
b) True but I am unsure of why
c) False but I am unsure of why not
d) False and I can explain why not

6. If A is not invertible and AB=AC then B=C sometimes but not always.
a) True and I can explain why
b) True but I am unsure of why
c) False but I am unsure of why not
d) False and I can explain why not

Solutions
1. a)
2. a)
3. b)
4. a)
5. a)