with explanation

6. Suppose that V is a subspace of R" and that 6'1, . . . ,6}. is a basis of V. Let A be the matrix with columns 171, . . . ,m Recall that the matrix of the orthogonal projection projV is B = A(ATA)'1AT. (a) Multiply B by itself, and show that B2 is equal to B. (b) Give a brief geometric explanation of (a), i.e., explain Why it's reasonable that applying B twice to a vector in R\" gives the same result as applying it once. (c) Show that B is symmetric, i.e., 3"" = B