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1.  If \(A\) is a 3 by 5 matrix, what is the maximum number of pivot positions A could have?

a.  0

b.  1

c.  2

d.  3

e.  5

2.  If \(A\) is a 3 by 5 matrix, what is the minimum possible number of free variables in the solution to the equation \(A\vec{x}= \vec{0}\)?

a.  0

b.  1

c.  2

d.  3

e.  5

3.  If \(A\) is a 3 by 5 matrix, then the equation \(A\vec{x}= \vec{0}\)

a.  must have at most one solution.

b.  may have at most one solution.

c.  can't have at most one solution.

4.  If \(A\) is a 3 by 5 matrix, then the solution to the equation \(A\vec{x}= \vec{0}\)

a.  might be a straight line through the origin.

b.  might be a straight line not through the origin.

c.  can never be a straight line.

5.  If \(A\) is a 3 by 5 matrix, then the solution to the equation \(A\vec{x}= \vec{0}\)

a.  might be a plane through the origin.

b.  might be a plane not through the origin.

c.  can never be a plane.

6.  If \(A\) is a 3 by 5 matrix and \(\vec{b}\) is a non-zero vector, then the equation \(A\vec{x}= \vec{b}\)

a.  must have a solution.

b.  might have a solution.

c.  definitely does not have a solution.

For questions 7 and 8, let $$A = \left[\begin{array}{cccc} 1 & 1 & 1 & 1\\ 1 & 2 & 3 & 4\\ 2 & 3 & 4 & 5\\ \end{array}\right]$$