31 on paper please FIGURE Ex-2930. What is the sum of all radial vectors of a regular n-sidegon? (See Figure Ex-29.)Working with Proofs31. Prove parts (a), (c), and (d) of Theorem 3.1.1.32. Prove parts (e)-(h) of Theorem 3.1.1.33. Prove parts (a)-(c) of Theorem 3.1.2. EXAMPLE 3 | Algebraic Operations Using ComponentsIf v = (1, -3, 2) and w = (4, 2, 1), thenv+w=(5,-1, 3),2v = (2,-6,4)-w = (-4,-2, -1),v-w=v+(-w) = (-3, -5,1)The following theorem summarizes the most important properties of vetions.Theorem 3.1.1If u, v, and w are vectors in R", and if k and m are scalars, then:(a) u + v=v+u(b) (u+v)+w=u+ (v + w)(c) u+0=0+u=u(d) u + (-u) = 0(e) k(u + v) = ku + kv(f) (k+m)u = ku + mu(g) k(mu) = (km)u(h) lu= uWe will prove part (b) and leave some of the other proofs as exercises.Proof (b) Let u = (U₁, U₂, ..., Un), V = (U₁, U₂, ..., Un), and w = (W1, W2,...,U(u + v) + w = ((U₁, U₂,..., Un) + (V₁, V₂,..., Un)) + (W₁, W₂,..., wn)[Vect== (U₁ + V₁, U₂+U2,..., Un + Un) + (W₁, W2,..., wn)= ((U₁ + v₁) + w₁, (u₂ + V₂) + W2,...,.., (un + vn) + wn)[Vect[Regr= (u₁ + (v₁ + w₁), U₂ + (V₂ + W₂),..., Un + (Un+wn))

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Answered: 31. Prove parts (a), (c), and (d) of…

31. Prove parts (a), (c), and (d) of Theorem 3.1.1.

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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In a study of high school students at least 16 years of age, researchers obtained survey results summarized in the accompanying table. Use a 0.05 significance level to test the claim of independence between texting while driving and driving when drinking alcohol. Are those two risky behaviors independent of each other? Click the icon to view the table of survey results. Determine the null and alternative hypotheses. Ho: H₁: Determine the test statistic. x² = (Round to two decimal places as needed.) Determine the P-value of the test statistic. P-value = (Round to three decimal places as needed.) Do the results suggest that texting while driving and driving while drinking are related? O A. Reject the null hypothesis. There is sufficient evidence at a 0.05 significance level to warrant rejection of the claim of independence between texting while driving and driving while drinking alcohol. Those two risky behaviors appear to be somehow related. B. Reject the null hypothesis. There is…
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