Algebra Consider the set (a, b) x (c, d) in R² , where (a, b)x(c, d) := {(x1, x2) E R² : a < x₁ < b, c < x2

Q: Let F= R and V = R*. Let W, = {(x1,x2,X3,X4) € R* : x1 – x2 + X3 – x4 = 0 and x1 +x2 = 0}, W2 =…

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Q: prove if x → y then xor y = y =

A: To prove : If x→y then x or y = y Lets use the help of truth table to prove the above statement.

Q: Let W = {(x, y) E R² : x, y > 0}. Define addition + of any two elements (x, y), (w, z) E W by (х, у)…

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Q: 13. Find the intersection of [x, y, z)=[-8,-3,-5]+[1,2,-1] and [x. v.]=[1.9,4]+s[2,1,7].

A: We can find the intersection of the curve .

Q: Find 4rye®y? dA, where R [0, 1] × [0, 2]. R

A: The objective is to find the double integration where  R=[0,1]×[0,2]

Q: Show that X is Hausdorff if and only if the diagonal △ = {(x, x)|x ∈ X} is closed in X × X.

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Q: Let  W = { (a, b) : a and b are real numbers, a + b =1 } . For any (a, b) and (c, d) in W and…

A: W={(a,b): a and b are real numbers, a+b=1} Since every vector space is a group under addition. If W…

Q: assume that Pr[A]=0.25Pr[A]=0.25, Pr[B]=0.35Pr[B]=0.35, and Pr[A∩B]=0.1Pr[A∩B]=0.1. 1)Pr[A|B] =…

A: Given: P(A) =0.25 P(B)=0.35 P(A∩B) =0.1

Q: Let u, ER" prove that ||ū + ï|| ≤ ||ū|| + ||v||

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Q: Let ƒ : Z → Z × Z be defined as f(n) = (2n, n + 3). Select which statements are true. a) for any in…

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Q: Find (a) ||u||, (b) ||v||, (c) u ∙ v, and (d) d(u, v).u = (1, −2, 2, 0), v = (2, −1, 0, 2)

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Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: Let ||u|| = 2, ||v|| = 3, (u, v) = 2+i. Compute ||u+v||², ||u-v||², (u + v,u - iv), (u + 3iv, 4iu).

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Q: Let A = {1,2,3} and let R= {(1,1), (2, 2), (3, 3), (1, 2), (2, 1), (3, 2)} C A x A. In each case,…

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Q: Sketch the set of points satisfying: |z - 1 + 2i| = |z + 3 + i|

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Q: Find (a) ||u||, (b) ||v||, (c) u ∙ v, and (d) d(u, v).u = (1, 4), v = (2, 1)

A: Since you have asked a question with multiple parts in a single request, we would be answering only…

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

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Q: |(u+ v) x (u – v)I = 2|u x v|

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Q: 2x + 1 3 – 4x Consider the function y = f(x) a) find Ax + h) simplify fully Ax + h) – Ax) h b) find

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Q: Let x(bar) = (3,-5,2,1,-2) element of R5. Find the norm of x(bar) using the usual norm on R5

A: The norm of x is the distance between a point x to the origin.

Q: prove that two vectur ae orthognal A = x + 4y+32 B =4x+2y-42

A: See the attachment

Q: a) What is the role of a and k in y = alx|+k?

A: Answered first question as per our company guidelines. Second question is incorrect please repost…

Q: rly). Let a) Evaluate r(20)

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Q: Evaluate f (x - y)(y - z) dV for the box B3 with dimension: [4, 9] × [0, 1] × [0, 1]. (Use symbolic…

A: We have to evaluate the integration .

Q: Prove: let v: X Y bijective then V inverse(v(x)) = X

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Q: Consider the algebraic identity (x + y)² = (x − y)² + 4xy By interepreting x, y as line segments,…

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