PSTAT 109 Lecture 4: Conditional Probability and Independence

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 vi=1 3 , V2= -7 , V3 = -6 1, V4= -7 6 and S = span{V1, V2, V3, V4}. Which one of the following statements is true? A) {V1, V2, V4} is a basis of S. B) dim(S) = 3. C) Any spanning set of S must contain 4 vectors. D) 3 is in S. -1 E) {V1, V2} is a basis of S.

16. Let T:R2 R2 be a non-zero linear transformation with standard matrix A, and let det(A) = 0. Which of the following statements is true? A) The parallelogram formed by T . and T0 ) has area 1. B) There is a linear transformation S: R2 + R2 such that SoT is the identity transformation. C) dim (span {7 ( 6 ) 7( ')}) – 1. D) For every vector b E R2, there is a vector u € R2 such that T(u) = b.