In mark each statement True or False. Justify each answer.
a. A homogeneous system of equations can be inconsistent.
b. If x is a nontrivial solution of Ax = 0, then every entry in x is nonzero.
c. The effect of adding p to a vector is to move the vector in a direction parallel to p.
d. The equation Ax = b is homogeneous if the zero vector is a solution.
e. If Ax = b is consistent, then the solution set of Ax = b is obtained by translating the solution set of Ax = 0.