If A is an m Times n matrix with m Solutiona True If the col

Solution

(a) True. If the columns span R^m, this says that every b in R^m is in the span of the columns, which is another way of saying that any b is a linear combination of the columns. Then the equation is consistent

(b) False. If Ax = b has a solution, it is unique if and only if every column of A is a pivot column. If every column of A is a pivot column, there are no free variables, and therefore the homogeneous equation has only the trivial solution