Let W be the set of all vectors of the form shown on the right, where a and b represent arbitraryreal numbers. Find a set S of vectors that spans W, or give an example or an explanation showingwhy W is not a vector space.-a +3a-4b3b + aSelect the correct choice below and, if necessary, fill in the answer box to complete your choice.O A. The set W is a vector space and a spanning set is S=(Use a comma to separate vectors as needed.)B.The set W is not a vector space because not all vectors u in W have the property 1u= u.O C.The set W is not a vector space because the zero vector is not in W.O D. The set W is not a vector space because not all vectors u, v, and w in W have the property that u + v=v+u and(u+v)+w=u+(v + W).

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Answered: Let W be the set of all vectors of the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The vector y is a numerical vector. Which ONE of the following best describes what the R code below will calculate? sum(!is.na(y)) A logical vector of the same length as the vector y, which takes the value TRUE for values in y which are NOT missing and FALSE for values in y which ARE missing. Replaces each value in y with TRUE if it is not missing and FALSE if it is missing The number of non-missing values in the vector y. The number of missing values in the vector y. The propostion of non-missing values in the vector y.
Questions 1-6. The table below represents the monthly unemployment rates in the US from January of 2005 through May of 2016. Year Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 2005 5.3% 5.4% 5.2% 5.2% 5.1% 5.0% 5.0% 4.9% 5.0% 5.0% 5.0% 4.9% 2006 4.7% 4.8% 4.7% 4.7% 4.6% 4.6% 4.7% 4.7% 4.5% 4.4% 4.5% 4.4% 2007 4.6% 4.5% 4.4% 4.5% 4.4% 4.6% 4.7% 4.6% 4.7% |4.7% 4.7% 5.0% 2008 5.0% 4.9% 5.1% 5.0% 5.4% 5.6% 5.8% 6.1% 6.1% 6.5% 6.8% 7.3% 2009 7.8% 8.3% 8.7% 9.0% 9.4% 9.5% 9.5% 9.6% 9.8% 10.0% 9.9% 9.9% 2010 9.7% 9.8% 9.9% |9.9% 9.6% 9.4% 9.5% 9.5% 9.5% 9.5% 9.8% 9.4% 2011 9.1% 9.0% 9.0% 9.1% 9.0% 9.1% 9.0% 9.0% 9.0% 8.8% 8.6% 8.5% 2012 8.2% 8.3% 8.2% 8.2% 8.2% 8.2% 8.2% 8.1% 7.8% |7.8% 7.8% 7.9% 2013 7.9% 7.7% 7.5% |7.5% 7.5% 7.5% 7.3% 7.2% 7.2% 7.2% 7.0% 6.7% 2014 6.6% 6.7% 6.6% 6.2% 6.3% 6.1% 6.2% 6.1% 5.9% 5.7% 5.8% 5.6% 2015 5.7% 5.5% 5.5% 5.4% 5.5% 5.3% 5.3% 5.1% 5.1% 5.0% 5.0% 5.0% 2016 4.9% 4.9% 5.0% 5.0% 4.7% Find the relative change in unemployment rate during 2015.
Let u4 be a linear combination of {u₁, U2, U3}. Select the best statement. ● A. {u₁, U2, U3, U4} is a linearly dependent set of vectors unless one of {u₁, U2, U3} is the zero vector. ● B. {U1, U2, U3, U4} is never a linearly dependent set of vectors. ● C. {U1, U2, U3, u4} could be a linearly dependent or lin- early dependent set of vectors depending on the vectors chosen. ● D. {U1, U2, U3, u4} is always a linearly dependent set of vectors. ● E. {U1, U2, U3, U4} could be a linearly dependent or lin- early dependent set of vectors depending on the vector space chosen. ● F. none of the above
Could a set of three vectors in R* span all of R*? Explain. What about n vectors in R™ when n is less than m? Could a set of three vectors in R* span all of R*? Explain. Choose the correct answer below. A. No. There is no way for any number of vectors in R* to span all of R. B. Yes. Any number of vectors in R* will span all of Rª Yes. A set of n vectors in R™ can span R™ when n

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