True/False: The set of vectors, is orthogonal.

Two vectors are orthogonal iff their dot product is zero.

True/False: The set of vectors, is orthogonal.

Two vectors are orthogonal if and only if their dot product is zero.

True/False: An orthogonal basis for a subspace of is a basis for that is also an
orthogonal set.

If is a basis for , then for any in , can be written as a linear combination
of . Given the vectors and below, compute the coefficients in the linear
combination.

. (Simplify fractions as much as possible.)

Let and . Find the orthogonal projection of onto .

First, find , then find .

Then the orthogonal projection of onto is .

Let be the line through and . The orthogonal projection of onto (or the
orthogonal projection of onto ) is

True/False: Not every orthogonal set in is linearly independent.

True/False: Every orthogonal set of non-zero vectors in is linearly independent.

What is the definition of an orthonormal set?

An orthogonal set that is linearly independent An orthogonal basis A basis
consisting only of unit vectors An orthogonal basis consisting only of unit vectors An
orthogonal set consisting only of unit vectors