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Unformatted text preview: Math 241 – Exam 1 – 2PM V1 September 22, 2008 55 points possible 3. (a) (4pts) Find the angle between the vectors a = 2 i + 2 j and b = 3 i + j + 4 k ). (b) (6pts) Find the area of the parallelogram formed by the vectors a = 2 i + 2 j and b = 3 i + j + 4 k ). 6. (a) (3pts) State the dot product definition for the length of a vector in R n . (b) (3pts) Clearly state the CauchySchwarz Inequality. (c) (4pts) Let a and b be vectors in R n . Use CauchySchwarz to prove the Triangle Inequality  a + b  ≤  a  +  b  . 4. Let A = • 4 0 5 1 3 2 ‚ . (a) (3pts) Consider the function F ( ~x ) = A~x , F : R n → R m . Clearly explain what the values of m and n are. (b) (3pts) Let ~a = (1 , 2 , 3). Compute F ( ~a ). (c) (4pts) Explain why the function F is a linear transformation. 2. (5pts) Find an equation of the plane containing the points ( 1 , , 4), (1 , 5 , 2) and (2 , 4 , 8)....
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This note was uploaded on 02/07/2010 for the course MATH 241 taught by Professor Any during the Spring '08 term at University of Illinois at Urbana–Champaign.
 Spring '08
 Any
 Math, Calculus, Vectors

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