A square matrix is called idempotent if (we write to represent ). Suppose that ( ) is a matrix such that is invertible. Prove that both and I_n-〖X〈X^' X〉〗^(-1) X^' are idempotent. (Hint: use this property of matrix multiplication: ).

You will get 25 points an image of a rectangular prism is shown below: part a: a cross section of the prism is cut with a plane parallel to the base. what is the name of the shape created by the cross section? explain your answer. (5 points) part b: if a cross section of the prism is cut perpendicular to the base, what would be the shape of the resulting cross section? explain your answer. (5 points)

Can someone me with #s 8, 9, and 11. with just one of the three also works. prove using only trig identities.

Which zero pair could be added to the function f(x) = x2 + 12x + 6 so that the function can be written in vertex form? o 3, -3o 6,629,-936, 36