1. Which of the following are true about M:=Matrix([[1,4],[2,5],[3,6]])? Note that when M is augmented with a generic vector and reduced to Gaussian, the last row becomes [0 0 b1-2b2+b3]
a) The column space is the plane b1-2b2+b3=0 in R3
b) The column space is the plane sVector([1,2,3]) + tVector([4,5,6]) in R3
c) The nullspace is the 0 vector in R2
d) more than one of the above, but not all of them
e) all of a), b), c)

2. If an matrix is not square, then
a) the column space is a subspace of Rnumber of rows
b) the column space is a subspace of Rnumber of columns
c) further work must be done to tell.

3. The definition of a basis is a linearly independent spanning set for V. Which of the following also describes a basis?
a) A basis is a minimal spanning set for V.
b) A basis is a largest possible set of linearly independent vectors in V.
c) An efficient way (linearly independent) to represent a space (span) linearly.
d) all of the above
e) two from a), b), c) but not all three

Solutions
1. e)
2. a)
3. d)