e406fk

e406fk - proving part of it This Quiz was the same as my...

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MAS 3105 Oct 25, 2006 Quiz 4 Prof. S. Hudson 1) [40 points] Set B = { v 1 , v 2 , v 3 , v 4 } = { (1 , 0 , 0) T , (1 , 0 , 1) T , (0 , 1 , 1) T , (0 , 0 , 1) T } . So, B is a set of 4 column vectors in R 3 . Answer, and explain briefly: a) Is B a spanning set of R 3 ? b) Is B linearly independent? c) Let C = { v 1 , v 2 , v 4 } . Is C a basis of R 3 ? d) Let D = { v 1 , v 2 , v 3 } . Show that D is a basis of R 3 . e) Find the transition matrix from D to the standard basis of R 3 . 2) [20 points] Choose ONE of these to prove (use the back). a) Show that a nonempty subset of a linearly independent set of vectors { v 1 , v 2 ,... v n } must also be linearly independent. [Use the definition of LI]. b) Show that if { v 1 , v 2 ,... v n } is a basis of V , and v V , then v can be written uniquely as a linear combination of { v 1 , v 2 ,... v n } . [Do NOT quote Thm 3.3.2 - you are
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Unformatted text preview: proving part of it]. This Quiz was the same as my Spring 2003 Quiz 4 (see that Key for answers). The average in 2006 was 45/60 (The average in 2003 was 41/60, and I may use this info to improve the scale). For now, the scale is: A’s: 51-60, B’s: 45-50, C’s: 39-44, D’s: 33-38 I estimated your semester average from your best 3 of 4 quiz grades, and wrote it on your Quiz 4 (upper right corner). This does not yet include HW or MHW. If you missed a quiz, and were excused, I have not yet adjusted for that, so your letter grade is probably not very accurate. 1...
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This note was uploaded on 12/26/2011 for the course MAS 3105 taught by Professor Julianedwards during the Spring '09 term at FIU.

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