11.10. EXERCISES 293

11. Suppose {v1, ..., vn} is a linearly independent set of vectors in an inner product space.The Grammian determinant is

det

(v1, v1) (v1, v2) · · · (v1, vn)

(v2, v1) (v2, v2) · · · (v2, vn)...

......

(vn, v1) (vn, v2) · · · (vn, vn)

Show this is not zero.