Infinite-dimensional vector space
Prove that the space P of all polynomials is an infinite-dimensional vector space. [Hint: mathematical induction may be useful here.]
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Let T be a linear transformation that maps Rn onto Rn. Show that T-1 exists and maps Rn onto Rn. Is T-1 also one-to-one? If so, prove it. If not, prove that instead.
Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. Find the probability that a randomly selected adult had an IQ greater than 131.5 (the requirement for membership in the Mensa organiz
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