h T/F? If detCA) = ac - b'2 > 0 and a > 0. then all the eigenvalues of A are positive. Q39 (Very Hard): T/F? We have at? + bey + cy'2 > 0 for any x and y, if the following matrix has positive eigenvalues: (Hint: Use 036.) hove-cotani-'JJOZI GdyoungCheong"' Q40 (Hard, but easier than Q31): Let A be a 2 x 2 matrix such that ' A is nonzero *A'2=0. Explain how to construct a 2 x 2 invertible matrix P such that P'{-1}AP is equal to 01 00 (Hint: Since A is nonzero, there must be a vector v in R'Z such that Av is nonzero. First, try to see why Av and v are linearly independent.)