All vectors and subspaces are in RnR n. Mark each statement True or False. Justify each answer.
a. Not every linearly independent set in RnR n is an orthogonal set.
b. If y is a linear combination of nonzero vectors from an orthogonal set, then the weights in the linear combination can be computed without row operations on a matrix.
c. If the vectors in an orthogonal set of nonzero vectors are normalized, then some of the new vectors may not be orthogonal.
d. A matrix with orthonormal columns is an orthogonal matrix.
e. If L is a line through 0 and if ˆyy^ is the orthogonal projection of y onto L, then ∥ˆy∥∥ y^ ∥ gives the distance from y to L.
