In mark each statement True or False. Justify each answer on the basis of a careful reading of the text.
a. The columns of a matrix A are linearly independent if the equation Ax = 0 has the trivial solution.
b. If S is a linearly dependent set, then each vector is a linear combination of the other vectors in S.
c. The columns of any 4 X 5 matrix are linearly dependent.
d. If x and y are linearly independent, and if {x, y, z} is linearly dependent, then z is in Span {x; y}.