(a) 0 solutions

(b) only 1 solution

(c) only a line of solutions

(d) only a plane a solutions

(e) other types of solutions

A reduced row-echelon form of a 3x4 augmented matrix can have how many leading 1s/pivots?

(a) must have 3

(b) may have 1, 2, or 3

(c) may have 0, 1, 2, or 3

(d) may have 0, 1, 2, 3, or 4

(e) must have 4

What about a 15x16 augmented matrix?

(a) the reasoning is similar - up to 15 leading 1s/pivots

(b) the reasoning is different

What about a 2x3 augmented matrix?

(a) may have 1 or 2

(b) may have 0, 1, or 2

(b) may have 1, 2, or 3

(c) may have 0, 1, 2, or 3

(e) none of the above

A reduced row-echelon form of a 2x4 augmented matrix can have how many leading 1s/pivots?

(a) must have 2

(b) may have 1 or 2

(c) may have 0, 1, or 2

(d) may have 0, 1, 2, 3, or 4

(e) must have 4

If a 2x4 system has at least one solution, then the geometry of the set of solutions may be

(a) a point

(b) a line or a plane

(c) all of R

(d) two of the answers above

(e) all of the above answers

A system of 2 equations and 2 unknowns and a system of 3 equations and 3 unknowns has 0, 1 , or infinitely many solutions.

(a) True

(b) False

(c) Sometimes true and sometimes false