6.1 Inner Product, Length, & Orthogonality(T/F)

v · v = |v|^2 .

true

For an m x n matrix A, vectors in the null space of A are orthogonal to vectors in the row space of A.

True

For any scalar c, u · (cv) = c (u · v).

True

If the distance from u to v equals the distance from u to -v, then u and v are orthogonal

True

If vectors v1, . .. , vP span a subspace W and if x is orthogonal to each vj for j = 1, ... , p, then x is in W _1_.

True

If x is orthogonal to every vector in a subspace W then x is in W_|_.

True

If ||u||^2 + ||v||^2 = ||u + v||^2, then u and v are orthogonal.

True

u · v - v · u = 0.

True

For a square matrix A, vectors in Col A are orthogonal to vectors in Null A.

False

For any scalar c, ||cv|| = c||v||

False