5 Let S v1 vp be a set of vector in Rn A v1 vp Determin

5. Let S = {v1, ..., vp} be a set of vector in Rn , A = [v1, ..., vp]. Determine which of the following in FALSE.

a. If S is L-I, then every column of A is a pivot column.

b. If S is L-I and p = n, then Ax = b is consistent for all b Rn .

c. If S is L-I, then every subset of S is L-I.

d. If S is L-I, then Ax = b can’t have more than one solution.

e. none of these

Solution

If S is L-I then every column of A is a pivot column then S is a linearly dependent set if and only if at least one element of S is a linear combination of the other elements.

Therefore (a) is false