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The linear tranformation L defined by L(p(x)) = -9p' - 6p" maps Pinto P. (a) Find the matrix representation of L with respect to the ordered bases E = {r", 1, 1,1} and F = {2? + +1, 2+1, 1} 0 0 0 S= 0 0 0 (b) Use Part (a) to find the coordinate vectors of L(p()) and L(g(x)) where p(r) = 2.r 13r and g(x) = r? - 5. [L(p()) = 0 L(g(x)) p = Submit answer
(a) Circle the logical statement that is equivalent to p→9. 9P ~pvq ~p~9 рл~ 4 (b) Write the negation of the conditional without using "ifand "then." If you are led by the Spirit, then you are not under the law. (Galatians 5:18)
Exercise 13. For each pair of polynomials p(x), q(x) E P define (p, q) р(«)q(2) dx. -1 inner product (i) Prove that (p, q) defines on P3 an orthogonal (ii) Show that 1, х are (iii) Find the angle between 1 and 1 + x. Exercise 13. For each pair of polynomials p(x), q(x) E P define (p, q) р(«)q(2) dx. -1 inner product (i) Prove that (p, q) defines on P3 an orthogonal (ii) Show that 1, х are...
If the r. v. X takes the values 1, 2, 3 and 4 such that 2P(X=1)-3P(X 2)-P(X-3)-5P(X-4) Find i) the probability distribution i) the smallest value of k for which P(X k)> ii) P(1.5<X-3.5| X 2)
Consider the differential operator T:P3(R)→P3(R) given by T(p(x))=2p″(x)−2p′(x)−2p‴(x) Find an ordered basis F for P3(R) such that T acts like a shift operator with respect to F, i.e. M??(?) (1 point) Consider the differential operator T : P3(R) → P3(R) given by T(p(x)) = 2p"(x) — 2p'(x) – 2p"(x) 1 Find an ordered basis F for P3(R) such that T acts like a shift operator with respect to F, i.e. MF(T) = 0 0 0 0 0 0 0 0...
4. The Pell sequence P, P... is defined by P-1, P-2, and P-P-2+2P- for n 3. Define T E C(R") by T(z, y)-(y,x + 2y). (a) Prove that T"(0,1) (PP+) for every integer n1 (b) Find the eigenvalues of T. (c) Find a basis of R2 consisting of eigenvectors of T. (d) Use the solution to part (c) to compute T (0,1. Hint: Write (0,1) as a linear combination of eigenvectors.] (e) Use your answers to parts (a) and (d)...
4 (10pl Assume you are gven the following equations for demend and supply o-13-2P P-2 a Calculate the equabrium price and quantity. :5-2 3 13-2P- P-2 53 Q-3 P5 b) Draw a diagram and show the producer and consumer surplus 13-2P 2P Go 13 G5 P-13-4p er Srp 55T 2 P 4.5+ sepl Calculate the consumer and producer surplus c 2 PS-153) CSSG.S-4) 12.5 PS=3 praducer urplus4 Consumer surpluG.25 d) Calculate the (own) price elasticity of demand and the (own)...
Suppose a random variable X has support {1,2,3,4,5} and that P(X = 1) = P(X = 2) = 2P(X = 3) = 2P(X = 4) = 3P(x = 5). Find the distribution of X and E[X]. .
4. Compute each probability or quantile 1 (а) X~ N(3, 0.0225), P(X < 3.25). (b) X~ N(52, 49), Р(X > 60). (с) X~ N(3.7, 4.55), Р(3.0 < х < 10.0). (d) XN(25, 36). Find the first and third quartiles for X.
x, y, and z are three independent Poisson random variables with the same mean. If P(x=1)=2P(x=0), what is P(x+y+z<=2)