(3 points) Observe that H1 = √ 1 2 +1 +1 +1 −1 is an orthonormal basis. Note that H2 = 1 2 +1 +1 +1 +1 +1 −1 +1 −1 +1 +1 −1 −1 +1 −1 −1 +1 can be written as a block matrix as H2 = √ 1 2 H1 H1 H1 −H1 , and an 8-by-8 matrix H3 can be defined as H3 = √ 1 2 H2 H2 H2 −H2 . Show that H2 and H3 are each orthonormal bases. (Hint: To show that distinct columns c1 and c2 have zero dot product, consider cases. Are c1 and c2 both among the left half ? The right half ? One of each? Also, does the √ 2 matter for zero dot products? )