In mark each statement True or False. Justify each answer.
a. The equation Ax = b is referred to as a vector equation.
b. A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax = b has at least one solution
c. The equation Ax = b is consistent if the augmented matrix [A b] has a pivot position in every row.
d. The first entry in the product Ax is a sum of products.
e. If the columns of an m X n matrix A span Rm, then the equation Ax = b is consistent for each b in Rm.
f. If A is an m n matrix and if the equation Ax = b is inconsistent for some b in Rm, then A cannot have a pivot position in every row.