- 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 b
_{1}-2b_{2}+b_{3}]

a) The column space is the plane b_{1}-2b_{2}+b_{3}=0 in R^{3}

b) The column space is the plane sVector([1,2,3]) + tVector([4,5,6]) in R^{3}

c) The nullspace is the 0 vector in R^{2}

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 R^{number of rows}

b) the column space is a subspace of R^{number 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
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)