Explain to Bryan and Rachel who's right. Make sure to point out any correct, incorrect, or partially correct statements they made. Your response should be addressed to Bryan and Rachel, and should help them understand the material for their test (that is, don't just say where they went wrong or what they did right, explain why).

Bryan and Rachel are studying for their MAT223 final exam. They are trying to find the eigenvalues 2 of the matrix A = 0 2 Bryan says the eigenvalues are 2, 1, and -1, because when you row-reduce, 2 1 No 0 2 R2+ + Ra 1 1 0 Ra-2R2 ON O 1 0 2 O you get an upper-triangular matrix, and so the eigenvalues are the numbers on the diagonal. Rachel says the eigenvalues are 2 and 1 because when you compute the characteristic polynomial of A, you get 2 - 1 2 char(A) = det 0 2-A -1 = (2 - A)(1-x)2. 0 Since the only roots of char(A) are 2 and 1, those are the eigenvalues. Explain to Bryan and Rachel who's right. Make sure to point out any correct, incorrect, or partially correct statements they made. Your response should be addressed to Bryan and Rachel, and should help them understand the material for their test (that is, don't just say where they went wrong or what they did right, explain why)