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223midterm20069

# 223midterm20069 - University of Toronto Department of...

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University of Toronto Department of Mathematics MAT223H1F Linear Algebra I Midterm Examination October 26, 2006 A. Esterov, M. Shub, S. Uppal Duration: 1 hour 50 minutes Last Name: Given Name: Student Number: Tutorial Code: No calculators or other aids are allowed. FOR MARKER USE ONLY Question Mark 1 /5 2 /5 3 /8 4 /10 5 /8 6 /10 7 /10 8 /4 TOTAL /60 1 of 12

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Indicate your answer for the true/false questions by shading in the box corresponding to your choice. Each correct answer is worth 1 mark. [5] 1. For each of the following statements, determine whether the statement is guaranteed to be true or is false. (a) For vectors u , v and w in R 3 , if u is orthogonal to v and v is orthogonal to w , then u is orthogonal to w . true false (b) If u and v are two vectors in R 3 , then there is a non-zero vector w span { u , v } which is orthogonal to u and v . true false (c) Let n be a vector in R 3 and let d 1 and d 2 be real numbers with d 1 = d 2 . Then the planes given by the vector equations n · p = d 1 and n · p = d 2 intersect in a line in R 3 .
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