Linear Algebra: Basis and Dimension

10. Find the coordinate vector of p relative to the basis S = {p1, p2, p3}.

(a) p = 4 - 3x + x2; p1 = 1, p2 = x, p3 = x2
(b) p = 2 - x + x2; p1 = 1 + x, p2 = 1 + x2, p3 = x + x2

22. Find the standard basis vectors that can be added to the set {v1, v2} to produce a basis for R4.

v1 = (1, -4, 2, -3), v2 = (-3, 8, -4, 6)

30. Prove: Any subspace of a finite-dimensional vector space is finite-dimensional.
Hint: You can do a proof by contradiction by using 2 or 3 Theorems from section.

See attached file for full problem description.

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Elisabeth Nicholson, PhD (IP)

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Active since 2006

BA in Anthropology and Mathematics, Barnard College, Columbia University
PhD in Evolutionary Biology, Northwestern University

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"Should Bold Italic each heading??"

"In your opinion, how long should the summary be?"

"Ok, here goes the re-write as per your suggestion: OLD:This is important to know and will require further research because the same occurrences in the Carver study does have a correlation between those who must have an HR degree in contrast who those with non-HR degree versus those with a professional certification in HR. The new re-write ::This is important to know and will require further research because the same occurrences in the Carver study does have a correlation between those who must have an HR degree to practice than for those with a non-HR degree who can still make a impact.:: You thoughts??"

"Hi Elisabeth, Thank you so much for your help! I was looking for help though with the manual calculations of the part below though so I would know how to do this problem, and cannot turn in my assignment with an online calculator used for the part below. Could you possibly answer the question below without the online calculator? We have to show our work. Thank you! A calculator to automatically solve these probabilities is here: http://www.vassarstats.net/textbook/ch5apx.html Fill in the table on that website with N = 4 and p = 0.5. Change the value of k to e 0, 1, 2, 3, and 4 to find the theoretical probabilities for each possible number of heads. They are: a. Zero Heads = 0.0625 = 6.25% b. One Head = 0.25 = 25% c. Two Heads = 0.375 = 37.5% d. Three Heads = 0.25 = 25% e. Four Heads = 0.0625 = 6.25%"

"Hi Nicole, I have chapter 2 (roughly about 20 pages) for editing, i.e., punctuation etc for your review. Are you still editing? Please advise."