Let V = {(a1, a2): a₁, a2 € R}. Define addition of elements of V coor- dinatewise, and for (a₁, 02) in V and c € R, define c(a₁, a2) = (0,0) if c = 0 [(ca₁, a²2) if c ‡ 0.

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: 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: 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: Let u = Al 2 [R and v= find a and b such that au + bv [:] 3

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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: Submit through Canvas as indicated. T u = (2,-5) and v= −3i+7j

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Q: What is u × w, assuming that w × u = 〈2, 2, 1〉?

A: Given,w×u=2,2,1 To find:u×w Solution: We know ,by property of cross product of two vectors (say,a…

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 = Compute the following: ū• v = (1, −5, −1) and v = (-5,2,0). v.u ||ū|| ² - 3 (u.v) (-3ū) v =…

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Q: en ủ × ʊ = (2, 3, 4), find (ũ − 4v) × (ũ + 3v).

A: Topic:- vector algebra

Q: Consider the following. u = (-5, 5, 4) v = (0, 1, 6) Find u x v.

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

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Q: Let y = Ա 4 + DIS 5 Ա and u = x³ = x³ - 2x.

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Q: Let V be the set of all pairs (x, y) of real numbers together with the following operations: (x₁,…

A: V be the set of all pairs (x,y) of real numbers  together with the following operations ;…

Q: Let A={2,y,z} and B={3,x,z}. How many distinct elements are in (A×B)∩(B×A)

A: Given, A={2,y,z} B={3,x,z} How many distinct elements are in (A×B)∩(B×A) ?

Q: Suppose (x1,x2) + (Y1,Y2) is defined to be (x1 + Y2 ,x2 + Y1). With the usual multiplication cx = (…

A: It is given that the addition is defined as x1, x2+y1, y2=x1+y2, x2+y1 and the multiplication is…

Q: Let ü = 21 – k and i = i + 3j + k. Compute |ū], |ū], ū × ĩ, and Projzu.

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Q: Let u=2i+3j-2k and v=-1i-4j +k Find u . v, ||u|| and u . v

A: Given that u and v vector and we find its dot product (u.v) and mode of u(||u||). Here i attached…