6. Let u = (1, 2, –3) and v = (4,0, –2). Compute u x v. 7. Let u = (2, 4, -4) and v = (1, –3, 1). Compute u x v. 8. Using the fact that u x v = (1, 1, 0), compute (u – 2v) x (u+ v). -

Q: Let u = (9,3,-3), v = (0,2,-5), and w = (6,5,4). Compute v X w. vxW=(

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

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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: Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies.…

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Q: Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies.…

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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: ppose S = &v₁₁ ore that T = nearly independ

A: Answer given below.

Q: Show that V spans P² where V = {1 + 2t + 2t², t + t², 1 − t²}

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Q: Let u = (-3, 1) and v = (0,3). Compute the following: u.v= • = | | i|| 2 = −1 (u · v) • (−1ū) · v ū⋅…

A: Step 1:Step 2: Dot Product (·):The dot product measures how much two vectors are aligned with each…

Q: u = [8, –1, –2] v = [0,7, 2] V u x v = [ Ex: 5

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Q: Find u x v, v × u, and v × v. u = i - j, v=j - k V (a) u x v (b) v x u (c) v x v

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Q: Let x 4 || - N and y = Find the vector v = 3x - 4y and its additive inverse. 18 [2] 4

A: The additive inverse of a vector v = <a , b> is  - v = <-a , -b>

Q: _3. Let x be a convex combination of {y1, . . , yk }. Assume in turn that each y; is a convex…

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Q: 8. Let V={(x,y)x,y € R}. Define addition on V as follows: (x»x)+(x,y)=(x +2x, 1,y+Y,+2) Find the…

A: To find zero vector of V

Q: Given u(x)= x +3 and v(x)= 9x – 4, find u v. O 9x² – 12 - O 9x² + 27x – 4 O 9x+ 23 x - 12 O 9x + 23…

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Q: are linearly independent if and only if k # -0-2-0 v= -6 -1 + k 3 = 5 1 1 7

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Q: Let R(s, t) = G(u(s, t), v(s, t)), where G, u, and v are differentiable, and the following applies.…

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Q: Q.4.(a). Show that the following functions is not an inner product on R3, where u = (u, U2, U3) and…

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Q: Let v (k,2k,1) and w (k,-1,-8). For which values of k are v andw orthogonal?

A: Calculation:Since it is given that v and w are orthogonal, v ∙ w = 0.

Q: Given u = (0,1, -1,2) and v = (1,1,3,0) find ||u + v||

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

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Q: 5. Let v = (2, 1, -4) and w = (3, -3, 1). Find vectors a and b such that v = a + b where a is…

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Q: 5. For which value of x do the following vectors form a linearly dependent set in R -1 y =|x, in- х,

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Q: Prove that u × 0 = 0 × u = 0.

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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 a = (3, −4, 9) (a) Find k such that b = (−2, k, −6) is parallel to a. (b) Find k such that b =…

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Q: a. Is S = {v1, V2, V3} linearly independent

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Q: 2-Express each function in the form u(x, y) + iv(x, y), where u and v are real, (c) ez2 (d) In(1+…

A: We have to write in u(x,y) and v(x,y) form.

Q: Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies.…

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Q: Let y = 7 and U-span(u), with u = x1 = x2 = -21 TT -4. Write y=x1 + x2, where x1 in U and x2 in U+.…

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Q: Let →a=⟨7,−5⟩ and b→=⟨1,3⟩. Compute the dot product. →a X →b=

A: Given a→ = 7,-5 and b→ = 1, 3. We have to compute the dot product a→·b→.

Q: 1. Let A={1,3,5,7}. Let f:A→Z be the function f={(1,2),(3,4),(5,6),(7,8)}. Let g:Z→Z be defined by…

A: Given, Set A=1,3,5,7 and a two functions f and g as follows, f: A → Z by f=1,2,3,4,5,6,7,8 g: Z →Z…

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…