Let u, v, and w be distinct vectors of a vector space V. Prove that if {u, v, w} is a basis for V, then {u + v, u + w, v + w} is also a basis for V. (Note: V is an arbitrary vector space, so you may not assume that u, v, and w are tuples.)

If the public debt of a country in 2009 was $10432000000000 and the budget for 2010 was in deficit by $201645000000, what was the public debt in 2010? do not include commas in your answer.

Successful implementation of a new system is based on three independent modules. module 1 works properly with probability 0.96. for modules 2 and 3, these probabilities equal 0.95 and 0.90. compute the probability that at least one of these three modules fails to work properly.

If eh = hg and hg=16, find the diameter of k