finalexamfall08

finalexamfall08 - Final Exam Math 235 Fall, 2008 Name:...

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Final Exam Math 235 Fall, 2008 Name: Instructor: Note that calculators are allowed. Time:2 hours 1. a: Write the system of equations in part b as a matrix equation. b: For what a b c does the system of equations have a solution? 5 y - z = a, 2 x + y + z = b, x + 3 y = c. c: Let A = 1 2 3 0 1 2 - 1 - 2 2 1 . Let B = ± 0 4 - 3 1 2 3 ² . Compute AB and BA if possible. If not possible , say why it is not possible. 1

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2. a: let V be a vector space. Deﬁne what a basis of V is. b: Is { 1 , x - 1 , x 2 - 1 } a basis of P 2 , the vector space of polynomials of degree less than or equal to 2. Why? Again note that explaining why is an important part of this question. 3. a: Let V, W be vector spaces. Deﬁne what it means for a function F : V W to be a linear transformation. b: Are the following linear transformations? Why? Note that the why part of the question is very important. b1:
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This note was uploaded on 11/22/2011 for the course MATH 255 taught by Professor Staff during the Spring '10 term at UMass (Amherst).

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finalexamfall08 - Final Exam Math 235 Fall, 2008 Name:...

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