m235_f11prac-page3

# m235_f11prac-page3 - R Y that is compute r(1 y(1 Compute...

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Express d = 0 @ 1 0 1 1 A as a linear combination of a, b, c. 9. Describe in words the kernel and image of the following linear transformations: a: Orthogonal projection of R 2 to the line y =5 x, b: T : R 3 ! R , ~ v 7! (1 , 2 , 3) · ~ v , c: Rotation about the origin of the plane by angle / 6 . 10. Find a vector in R 3 orthogonal to both ( - 1 , 1 , 2) and (2 , 1 , 0) . 11. A town has two baseball teams, one named R and one named Y .E a c hs e a s o n6 0% of the fans of R stick with R and 40% switch to Y. Each season 80% of the fans of Y stick with Y and 20% switch to R. The total number of fans stays constant from season to season. Let r ( n ) ,y ( n )denotethenumbero ffanso f R,Y during season n . Find a matrix M = ab cd so that r ( n +1) y ( n +1) = ab cd ◆✓ r ( n ) y (
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Unformatted text preview: R, Y, that is, compute r (1) , y (1) . Compute r (2) , y (2) . 12. Let f : R 3 ! R 5 be a linear map. We are given that f ( u ) = (0 , 1 , 2 , 3 , 4) f ( v ) = (-1 , 2 , 6 , 1 , 4) . What is f (2 u-3 v )? 13. Which of the following are subspaces of the indicated space. Explain your answer. a: The set of of solutions in R 3 to the equation 3 x-y + 2 z = 1 . b: The set of vectors in R 4 orthogonal to (1 , 2 , 3 ,-4) . 14. The matrix M of size 4 ⇥ 6 has two free variables. How many leading ones does the RREF of M have? 15. Let A = ✓-1 2 ◆ , B = ✓-1-4 4 7 ◆ . Find a 2 ⇥ 2 matrix X so that AX = B. 3...
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## This note was uploaded on 11/22/2011 for the course MATH 235 taught by Professor Markman during the Fall '08 term at UMass (Amherst).

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