. True or false?
(1) There is at most one pivot in any row.
(2) There is at most one pivot in any column.
(3) There is at least one pivot in any row.
(4) There is at least one pivot in any column.
(5) There cannot be more free variables than pivotvariables.
(6) There is a linear system that has exactly two solutions.
(7) The weights c1, ..., cp ? R in a linear combination c1v1 +... + cpvp cannot all be zero.
(8) Given nonzero vectors u, v in R n , span{u, v} contains theline through u and the origin. Hint: can you describe this line asa set of vectors?
(9) Asking whether the linear system corresponding to a1 a2 a3 bis consistent, is the same as asking whether b is a linearcombination of a1, a2, a3.
(10) If the augmented matrix of a linear system has twoidentical rows, the linear system is necessarily inconsistent
