In mark each statement True or False. Justify each answer.

a. A homogeneous equation is always consistent.

b. The equation Ax = 0 gives an explicit description of its solution set.

c. The homogeneous equation Ax = 0 has the trivial solution if and only if the equation has at least one free variable.

d. The equation x = p + tv describes a line through v parallel to p.

e. The solution set of Ax = b is the set of all vectors of the form w = p + vh, where vh is any solution of the equation Ax =