Let e, f, h € Zt. If [e, f, h](e, f, h) = efh, then prove that (e, h) = 1.

Q: let v = (1, 3, −2) and w = (2, −1, 4). Compute v × w.

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Q: Consider the net revenue function given by S(p, u, v) = R(p, v) – E(p, u) in our usual notation.…

A: Use this net revenue function to determine the correct option.

Q: Let A=(1, 0), B=(0, 1), C=(1, 1), and D=(r, 1). Verify that R(A, B, C, D) = r.

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Q: Prove that A u (B n C) = (Au B) n (A u C).

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Q: Suppose , t2, ., , are linearly independent. Prove that S is linearly independent where (a) S=…

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Q: Suppose that x, y, z are functions of the independent variables u, v, w. Which of the following…

A: It is given that, x,y,z are a function of the independent variables u,v,w. Here we have to find…

Q: Let u (9, 9, 8) and = (-9, -1, - 8). = Find proj, (u). -

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Q: Let T : R? → R² such that T (1,0) = (3, 1), and T (0, 1) = (-1,3). Find T (2, 5). T (2, 5)=( (enter…

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Q: Let u = (5,-5, -7) and 7 = (-6, 1, 2). Compute the following: úxv= v X ū= úxu 3 (u xv) = ū × (30) =…

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Q: Let V = span{e2", xe2", x²e?=}. (a) Show that (a1e2a + a2xe2" + a3x²e2") e V for any a1, a2, az E R,…

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Q: Show that is isomorphic to Z2.

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Q: Let S= {n | n=5 k+ 4 for some integer k} Let T= {n|n=5 j– 1 for some integer j}

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Q: (2) Suppose that G, C Zn-r. Then prove that G,-1C Zn-r+1

A: We prove that

Q: Set f(a,b) = (1+ a + b) + (2 + 2a + b)x + (1 + a + 26)r² and F = {f(a, b) : a,b e R} a subset of…

A: Given that fa,b=1+a+b+2+2a+bx+1+a+2bx2 and F=fa,b : a,b∈ℝ is a subset of ℝ2x. The objective is to…

Q: u = [2, 6, –5] and v= [-3,–1,6] %3D A · A + (A + ng-) · (A x n)

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Q: Let z=x+iy  Let w=a+ib

A: To prove the equality of the two given angles

Q: ) Find the length of the curve determined by 7 (t) = 2t7 + V3t27 + t

A: To find the length of the curve

Q: Verify that ||v-w||^2=1 when ||v||=2, ||w||=1, and v*w=2

A: By the definition of inner product and norm we can derive the following formula : ‖u-v‖2=⟨u-v,u-v⟩…

Q: Show that <a, b | a5 = b2 = e, ba = a2b> is isomorphic to Z2.

A: We have to show that <a, b | a5 = b2 = e, ba = a2b> is isomorphic to Z2.

Q: Show that (AB)T and BTAT are equal.

A: Now,

Q: Prove that u × (v + w) = (u × v) + (u × w).

A: Here the objective is to prove that

Q: Let S={(0,-1,1),(0,-2,-1),(1,1,2)}.

A: S?

Q: Let fi = 1+x + x² + x³ , f2 = 1 + 2x + 3x? + 6x³, f3 = 3+2x + ? + 5x4, and g = 1+x + 2a? + tæ³. For…

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Q: k – 1 k+1 Let h : Z → Q × Q, given by h(k) : 2 2 Let G = {(m, m +1) | m E Z}. Show that G C h(Z).

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Q: A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8…

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Q: how that ℝ3 = span( 1 1 2 1 2 1 0 3 -1

A: We want to show that  any vector can be written as linear combination of the three  given vectors…

Q: 2. Let X ~ U[0, 1] and Yn = X. Prove that Y, 4x.

A: Given that, X~U0,1 Yn=n-1nX

Q: Suppose that T :C C is R-linear. Show that T is C-linear if and if T(iz) = iTz for all z.

A: First we describe the definition of C-linear function:

Q: 5. Let u= 2 and v= 2 find a and b such that au+by = 0 3

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Q: Let x, y € Z. Prove that if 2 | (x² - y2) then 4 | (x² - y²)

A: We know that the sum of two odd numbers is an even number.Also, the difference between two odd…

Q: Prove that if A C R and t > 0, then |A| = |AN(-t,t)|+|AN (R\(-t,t))|-

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