- 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)
- 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.
- 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
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