Math Help - Cauchy Schwarz question

I have no idea to start. I'm struggling so much in this class. Can someone help me out?

(a) Given that x² + y² + z² = 1, use the cauchy-schwarz inequality to find the largest possible value of the expression 2x + 3y + 6z

(b) Let A be a diagonalizable matrix, all of whose eigenvalues are either 0 or 1. Show that A² = A

thanks in advance!

If A = (2,3,6) and B = (x,y,z), then


is the expression you want to maximize.

Cauchy Schwarz says





so


or


For the 2nd, try




since D has only diagonal elements 0 or 1.

(b)Since A is a diagonalizable matrix, there exist invertable matrix B and diagonal matrix D( whose diagonal elements are 0 or 1), such that
.
since , that is,

combined with B is invertable, gives the result.