Suppose T : R4 →R4 with T(x) = Ax is a linear transformation such that • (0,0,1,0) and (0,0,0,1) lie in the kernel of T, and • all vectors of the form (x1,x2,0,0) are reflected about the line 2x1 −x2 = 0. (a) Compute all the eigenvalues of A and a basis of each eigenspace. (b) Is A invertible? Explain. (c) Is A diagonalizable? If yes, write down its diagonalization (you can leave it as a product of matrices). If no, why not?

(50 ) mrs. julien’s and mrs. castillejo’s classes are selling cookie dough for a school fundraiser. customers can buy packages of macadamia nut chip cookie dough and packages of triple chocolate cookie dough. mrs. julien’s class sold 25 packages of macadamia nut chip cookie dough and 30 packages of triple chocolate cookie dough for a total of $221.25. mrs. castillejo’s class sold 5 packages of macadamia nut chip cookie dough and 45 packages of triple chocolate cookie dough for a total of $191.25. (a) write the system of equations that model the problem. be sure to explain which equation represents which situation. (b) find the cost of each type of cookie. show your work. (c) explain which method you used to solve the system and why you chose that method.