In Exercises 21 and 22, mark each statement True or False. Justify each answer on the ba...

In Exercises 21 and 22, 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 × 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}