Q27: T/F? The vectors u_1 = e_1 + e_2 and u_2 = e_1 - e_2 are orthogonal to each other (in R*2). If it the statement is true, write v in Q26 as a linear combination of u_1 and u_2. (edited) Q28: Let u and v be nonzero vectors in R*2. What is the acute angle between u and v where the length of u + v is maximized? Q29: T/F? The distance between two nonzero vectors is O if and only if the two vectors are equal. Q30: T/F? Let A be any 2 x 2 nonzero matrix such that A*2 = 0. Then A must be similar to 01 00 Q31 (Very Hard): Let A be a 3 x 3 matrix such that * A"2 is not the zero matrix while * A 3= 0. Explain how to construct a 3 x 3 invertible matrix P such that P*{-1}AP is equal to 010 0 01 000 (Hint: Since A*2 is nonzero, there must be a vector v in R*3 such that A*2v is nonzero. Argue that A*2v, Av, v are linearly independent and construct P using these vectors.) (edited)