- If B-C = 0, what reasoning is used to show that B=C?

a) additive inverse

b) additive identity

c) associativity

d) exactly 2 from above

e) all of a, b, c

- If the product of two matrices equals the 0 matrix, then

a) one of the matrices has to equal the 0 matrix

b) both matrices have to equal the 0 matrix

c) neither a nor b

- If A is a square matrix and Ax=b has infinite solutions for 1 vector b,
then

a) A is not invertible and I have a good reason why

b) A is not invertible but I am unsure of why

c) A is invertible but I am unsure of why

d) A is invertible and I have a good reason why

e) There is no way to tell whether A is invertible without more information

- If A is a matrix that is NOT square
and Ax=b has infinite solutions for 1 vector b, then which best describes A:

a) Ax=b must always have infinite solutions

b) Ax=b can have 0, 1 or infinite solutions

c) Ax=b can have 0 or infinite solutions

d) Ax=b can have 1 or infinite solutions

- Let T: x ---> Ax be given as a linear transformation arising from a
square 2x2 matrix A. Assume that the set of all
outputs b (from Ax=b) is a line. What can we deduce?

a) The columns of A do not span R^{2} and I can think of an example

b) The columns of A do not span R^{2} and I can not think of an
example

c) A is onto R^{2}

d) The columns of A do not span R^{2} and A is onto R^{2}

e) None of the above statements are true