Check the true statements below:

a. the orthogonal projection of yy onto vv is the same as the orthogonal projection of yy onto cvcv whenever c≠0c≠0.

b. if the columns of an m×nm×n matrix aa are orthonormal, then the linear mapping x→axx→ax preserves lengths.

c. if a set s={}s={} has the property that ui⋅uj=0ui⋅uj=0 whenever i≠ji≠j, then ss is an orthonormal set.

d. an orthogonal matrix is invertible.

e. not every orthogonal set in rnrn is a linearly independent set.