Mark each of the following statements true or false:
(a) Every system of linear equations has a solution.
(b) Every homogeneous system of linear equations has a solution.
(c) If a system of linear equations has more variables than equations, then it has infinitely many solutions.
(d) If a system of linear equations has more equations than variables, then it has no solution.

(e) Determining whether b is in span(a₁, . . . , a_n) is equivalent to determining whether the system [A I b] is consistent, where A = [a₁.........a_n].
(f) In R³,span(u,v) is always a plane through the origin.
(g) In R³, if nonzero vectors u and v are not parallel, then they are linearly independent.
(h) In R³, if a set of vectors can be drawn head to tail, one after the other so that a closed path (polygon) is formed, then the vectors are linearly dependent.
(i) If a set of vectors has the property that no two vectors in the set are scalar multiples of one another, then the set of vectors is linearly independent.
(j) If there are more vectors in a set of vectors than the number of entries in each vector, then the set of vectors is linearly dependent.