• Let (A1, B1) and (A2, B2) be two Dedekind cuts of Q. Let C = A1 + A2 := {q1 +q2 : 91 € A1, q2 E A2}, D= Q\C. Show that (C, D) is a Dedekind cut of Q. (This defines addition of real numbers.)

Q: Let a = (5, 5, - 3) and b = ( – 5, 3, 0). Find the projection of b onto a. proj¡ b = <

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Q: Let g(x) = b,x² + bx + b,x + bg, x E R be a polynomium whose graph intersects the points (-2, 4),…

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Q: 02 Define a Map L: M232M.3 by 1 3. LHA)-1 A, Is L a L2 lincar transformotion? Pove yovy AssertionB

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Q: Q2:- Evaluate / x + ydA where Ris the trapezoidal region with vertices given by R 5 5 (0,0), (5, 0).…

A: To find - Evaluate ∬Rx + y dA where R is the trapezoidal region with vertices given by…

Q: Let X=ℝ2 and define d,:ℝ2×ℝ2→ℝ d2((x1 ,y1),(x2,y)2)) = max{|x1 - x2|,|y1 - y2|}. Draw the…

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Q: Use the Side Splitter Theorem 7 Maris.comm 14 3.5 2. 4.

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Q: A natural cubic spline is defined by Sa,(x-1)' +b,(x-1)² +c, (x - 1) + d, S(x) =- if 0sxs1 (x- 1)' +…

A: Step:-1 Since, we know for cubic spline S(x)=S0x=a0x3+b0x2+c0x3+d0…

Q: 23. Prove that (xo, Yo), (x1, y1), and (x2, y2) lie on a line if and only if (х — Хо)02 — Уо) - (*з…

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Q: 1) If the rational preferences of a consumer over bundles of (x₁, x₂) satisfies which of the bundles…

A: Solution of the problem as follows

Q: (a) Find the length of the projection of w onto v given that w = (4,7) and v = (1,1).

A: Given: w=4i+7j, v=i+j we know that projectionp→ of w onto v is given by p→=w.→v→v→2v→

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Q: 2. Find the images of the mapping W= z2 of the line y = 2.

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Q: ZA'B'C' is the image of LABC following the reflec- tion of ZABC across line (. If mZA'B'C'= + 20 and…

A: Given: m∠A'B'C'=x5+20, m∠ABC=x2+5 We know that when we take reflection of a triangle across any line…

Q: (d) Compute the cross product (0, 2, 1) × (1, 3, 1).

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Q: * Consider a piecewise linear interpolation of exp(x), O<=x<=2, with h=0.01; that is, split [0,2]…

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Q: The transformation (x, y)(-x, y) reflects the preimage across the diagonal line y = x. O True O…

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Q: Let X,X2, ,X, be a ranc *(X), = 0*(1– 0)1-x; %3D

A: from above distribution is binomial  f(x)θ=θx(1-θ)1-x  ;0&lt;x&lt;1 E(x)= nθvar(x)=nθ(1-θ)…

Q: Suppose that the three numbers r1, r2, and r3 are dis- tinct. Show that the three functions…

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Q: Find the point E that partitions the directed segment CD in a ratio of 1:5, given the points (4.-2)…

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Q: c If in is an involution of X, show that (r, y)in = (yi", rin) is an involution of X12). %3D

A: Given X is a lattice. Given in  is an involution of X To show: x,yin=yin,xin is an involution of X2…

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Q: Determine the ratio of the directed line segment AB when partitioned by point P. (Hint: A is the…

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Q: Let f(r, y) = |r|+ lyl- (a) Draw three r-cuts of f(r, y), three y-cuts of f(x,y), and one z-cut.…

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Q: How many distinct linear arrangements can be made by using the following shapes?

A: The number of shape are given above in the question.

Q: 1. Decide if the following statement is True or False: %3D Let A1, A2, ..., Ak E Mnxn(R) be such…

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Q: The image of the line Im(z) = -2 under the mapping f(z)= i(z) is

A: Solution:

Q: Give the Dedekind cuts in ℝ ≥0 corresponding to the following. Your definition should not refer to…

A: Consider two subsets L (lower) and U (upper) such that the pair of subset L, U  is a Dedekind cut if…

Q: 10 What are the coordinates of the point on the directed line segment from K(-5,-4) to L(5, 1) that…

A: Use mid section formula for evaluating the coordinates of points.

Q: Prove that y, + y, +2y, 56 is a valid Gomory cut for the following feasible region. X-{yeZ: 4y, +5y,…

A: We have, y2+y3+2y4≤6 X=y∈Z+4 ;X=4y1+5y2+9y3+12y4≤34X=y∈Z+4 ;X=5y2+9y3+12y4+5y2≤34X=y∈Z+4 ;…

Q: . Give the Dedekind cuts in R 20 corresponding to the following. Your definition should not refer to…

A: Given: 10 23 23+3 To find: Dedekind cuts in ℝ≥0 for the given real numbers.

Q: Queshon 6) Compute the arthogonal projection of 8 onto the Line L through -S] and the origin. -6 LS.

A: We have to find the orthogonal projection of v on the line through P and the origin.

Q: c If in is an involution of X, show that (x, y)in = (yin, xin) is an involution of X2). %3D

A: Let X be a lattice We have to show that (x, y)in=(yin, xin) is an X[2] X[2] is a 2 x 2 matrix We…

Q: Let a and b be nonzero and f(x, y) = (ax + by)e-x Show that if a ± b, then there are five critical…

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Q: Show that if α and β are Dedekind cuts, then so is α + β = {r1 + r1 : r1 ∈ α and r2 ∈ β}.

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Q: Figure ABCD maps to WXYZ with the following transformations:…

A: Let the coordinates of ABCD be represented by x,y. The transformations are given by:…

Q: 10 What are the coordinates of the point on the directed line segment from K(-5,-4) to L(5, 1) that…

A: We have to find out coordinates

Q: (a) express ux, u y, and uz as func-tions of x, y, and z both by using the Chain Rule and by…

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Q: A line l in P" is a one-dimensional projective variety of the form { = 5. V,(f1,..., fr), where each…

A: From the given information. The line l in  is a one-dimensional projective variety of form, .

Q: A chow that the wsonskian d es will neves become zex0 to8 all spal

A: Here we use the fact ex&gt; 0 ,for all real x.

Q: Let A € R"Xm, n > m. a) Use the SVD of A to deduce the SVD of AT A. b) If m = n and A is full-rank,…

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Q: The elimination of ci and c2 gives the relation Yk 1 1 2 0, (1.53) Yk+1 4 Yk+2 25 which, on…

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Q: Construct a linear map L(z) = az + 6 that will send the imaginary y-axis to the line v = - u

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Q: Let F(x, y, z) = (z, x, y), ar (0,0,0), (0, 1, 1), vertices are ar

A: Introduction: Stroke's theorem is simply a higher-dimensional version of Green's theorem. The line…

Q: Give a planar drawing of K2.3 with partition ({v1, v2}, {w1, W2, W3}).

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Q: • Let (A1, B1) and (A2, B2) be two Dedekind cuts of Q. Let C = A1 + A2 := {q1+q2 : q1 € A1, q2 E A2…

A: Second statement:      Let (A1, B1) and (A2, B2) be two Dedekind cut of ℚ such that 0∈A1, 0∈A2  and…

Q: We learned how to construct the map ² (V) → VV that sends the simple wedge V₁ V₂ → V₁ V₂ V₂ V₁ -…

A: Given that the map Λ2V→V⊗V is defined by the function, v1 Λ v2→v1⊗v2-v2⊗v1 We are asked to prove…

Q: How many points and lines does a finite projective plane of order 7 have?

A: The number of points in a projective plane of order n is n2+n+1. The number of lines in a projective…

Q: Let (A, B, C, D) be an ordered quadruple of distinct collinear points in II. Let G = S4((A,B,C, D))…

A: Given that (A,B,C,D) is an ordered quadruple of distinct collinear points.   Also given a set…

Q: Find the point O that partitions the directed segment MN in a ratio of 2:3, given the points…

A: The coordinates for the directed line segment MN¯ are M(-3, -2) and N(4, 2) Point O is the point…