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Material Type: Quiz; Professor: Bergvelt; Class: Applied Linear Algebra; Subject: Mathematics; University: University of Illinois - Urbana-Champaign; Term: Summer 2009;
Typology: Quizzes
1 / 3
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Quiz 3, Math. 415, Wednesday, June 24th, 2009 Explain your answers carefully. Write complete sentences, not just formulas. 1.a (10 points) Consider the permutation matrix
P =
What is the inverse of P?
1.b (10 points) Let x, y be column vectors (of the same length). Express the dot product x · y in terms of the transpose.
1.c (10 points) Explain why P x · P y = x · y if P is a permutation matrix.
2
a. (10 points) S is the set of vectors b =
b 1 b 2 b 3
, with b 1 = 1.
b. (10 points) S is the set of vectors b =
b 1 b 2 b 3
, with b 3 = 0.
c. (10 points) S is the set of vectors b =
b 1 b 2 b 3
, with b^21 + b^22 + b^23 = 1.
