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1. Let V be a vector space and F: V R a linear map. Let W be the subset of V consisting of all elements v such that F(v)=0. Assume that W V, and let be an element of V which does not lie in W. Show that every element of V can be written as a sum w + c , with some w in W and some number c.
2. In exercise (1), show that W is a subspace of V. Let { } be a basis of W. Show that { } is a basis of V.
Increasing the logarithmic expression
how do you find all the points having an x-coordinate of 3 whose distance from the point -2 -1 is
Explain what an inverse function is and how you can determine when an inverse function will exist. What procedure is available to determine if two functions are inverses of each other? Explain its use and give an example.
a rational expression is a fraction of two polynomials. if you need to add or subtract two rational expressions how
Fields are an important algebraic structure, and complex numbers have that structure - verify that the fifth roots of unity form a group under complex multiplication, showing all work.
Find the stable range of gains. Using MATLAB, plot: Bode plot (gain margin, phase margin). Nyquist plot (gain margin, phase margin). Root Locus.
Using these data, construct for x- and R-charts. Is the process in control? What other steps should the QC department follow at this point?
Finding the new coordinates of the point P.
How much farther will a ball travel for each mile-per-hour increase in the speed of the bat?
Find the solution for x
Set up the equation to solve the equation.
Single women. The percentage of women in the 20-24 age group who have never married went from 55% in 1970 to 73% in 2000 (Census Bureau, www.census.gov). Let 1970 be year 0 and 2000 be year 30.
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