STAT 4202 Lecture 14: Recitation 3 - 1.24.19

13. If the matrix expression ABT - (CA-1)T is defined, where A is n xn invertible, B is p xs, and C is q xt, then only one of the following is a necessary restriction on n, P, 8, 9, and t. Indicate which one. A) B) n=p=s=q=t. n=s=q and p=t. n=s= t and p=q. P=s=n and q=t. D)

4. An equation of the plane containing the point P(1,-1,2) and perpendicular to the line (x, y, z) = (2-3t, 1+ 5t, 7+t) is (A) 2.0 + y + 72 = 15 (B) 6:- 10y - 22 = 12 (C) 4.2 - 9y - 62 = 1 (D) 92 + 5y - 22 = 0 (E) 3x + 2y - 2= -1

2. Let A= 3 S 03 [it] BE where s and t are real numbers. [ 0 -2] Which one of the following statements is true ? (A) A is diagonalizable for all s, and B is diagonalizable only if t = 0. (B) A is diagonalizable if s= 0, and B is not diagonalizable if t +0. (C) A is not diagonalizable if s 70, and B is diagonalizable for all t. (D) A and B are both diagonalizable for all s and all t. (E) A and B are diagonalizable only if s= 0 and t = 0.