The system has
(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 R³
(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