COURSE MATH 3191-004: Applied Linear Algebra. Fall 1994. University of Colorado Denver INSTRUCTOR Dr. Andrew Knyazev Office: CU (Dravo) 620G. Phone: 556-8102. Office hours: Tue 3pm - 6pm EXAM #2 (Chapters 2-3) 20% of the FINAL GRADE Wednesday, October 26 2 0 0 2 Let A be the following matrix 1 1 0 1 for problems 1-4. 1 2 2 1 2 0 0 1 1. det(A) = [A] 0 [B] 1 [C] -4 [D] -2 2. Which of the following is an eigenvector of A? [A] (0 0 0 0) [B] (0 1 0 0) [C] (0 -1 2 0) [D] The correct answer is not given by [A],[B], or [C] 3. det( adj(A)) = [A] 0 [B] 1 [C] -64 [D] -1 4. Let B = A+A , and C , C be cofactors of the matrix B. Then [A] 0 [B] 1 [C] -1 [D] -2 5. The expression +a a a a a a a is a signed elementary product from a 7x7 matrix A if [A] i=1, j=2 [B] i=2, j=6 [C] i=6, j=6 [D] i=6, j=2 6. Which of the following statements must be true: [A] If det(A) = det(B) = 0, then det(A+B)=0. [B] det(ABC)=det(BCA)=det(CAB) for square matrices A,B, and C of the same sizes. [C] Both [A] and [B] are correct statements [D] None of the above is correct 7. Let vectors u=(1 2 3) and w=(3 2 1). Then cos { proj u, proj w } = [A] 5/7 [B] 7/5 [C] -5/7 [D] The correct answer is not given by [A],[B], or [C] 8. Let u and w be two orthogonal unit vectors in 3-space. Then the volume of the parallelepiped determined by the vectors u, w, and u w equals to [A] 0 [B] 1 [C] -1 [D] The correct answer is not given by [A],[B], or [C] 9. Find the distance between the given parallel planes -4x+y-3z=-1 and 8x-2y+6z=0 [A] 0 [B] 1 [C] -1 [D] The correct answer is not given by [A],[B], or [C] 10. Find the equation of the plane passing through the point (1,2,-1), (2,3,1) and (3,-1,2). [A] -1x+y-3z=-1 [B] 9x+y-5z=-16 [C] Such a plane does not exist [D] The correct answer is not given by [A],[B], or [C]