Please answer all of there problems, and explain every step. True or False (give

Question

Please answer all of there problems, and explain every step.

True or False (give justification): The function T(f) = 2f - 4f? + 3f?? is a linear transformation from C infinity (R) to C infinity (R). True or False (give justification): There exists a linear transformation T : P5 rightarrow P, from the space of ALL polynomials with real coefficients to the space of degree 5 polynomials with real coefficients, whose kernel is trivial (contains only the zero-vector). Let L be the line in R3 given by the L = {r· (3, l, 2) | r epsilon R}, and let p = (1,1,1). Determine the point q epsilon L closest to p and compute the distance between q and p. Consider an inner product upsilon, omega on a vector space V, and a scalar k epsilon R. For which choices of k does upsilon, omega := k upsilon, omega define an inner product?

Explanation / Answer

4.true

5.false

6.true

7false

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