Let f be a function that takes elements of R?rR? into R' as follows: f(u, v) = |u1v1|+ |u2v2|, where u = (u1, u2) E R² and v = (v1, v2) E R². Show that f cannot be an inner product by showing that one of the properties is not satisfied.

Q: Consider the function of two variables defined by: f(x,y) = (x3 - y4) / (x-7210)2+(y-9245)2 What…

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Q: Let In, f be real fun ction on 52.Show {w : fu(w) yo frw) }=Ŭ o U {w-1fu(w) %3D f(w)1>と3

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Q: Show that f[x0, x1, x2] = f[x2, x1, xo].

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Q: Consider a function with three variables a, b, c s.t f(a,b, c) = 2abc – a²b +c²b³c Find fa (a, b,…

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Q: Let f(x, y) /150- 4а2 — 2у? 4x? – 2y? Evaluate f(1, 3)

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Q: Consider the function of two variables defined by: f(x,y) = (x3y4) / (x-7210)2+(y-9245)2 What…

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Q: Find the adjoint of F:C3 tends to C3 defined by F(z1, z2, z3)=(2z1+(1-i)z2 , (3+2i)z1 -4iz3 ,…

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Q: Determine if F = x²yî + (xyz +29)ĵ – x²y²k is conservative or not %3D

A: For vector field F⇀=ui^+vj^+wk^ Curl(F)=i^j^k^∂∂x∂∂y∂∂zuvw   For vector field F⇀ to be conservative…

Q: Consider the function ƒ (x, y, z) = 2x² + 5y² + z². a) If ƒ (x, y, z) is the profit made from…

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Q: Let /: X →Y be a function, A, BC X and C, DCY. Show that: 1. f(AUB) = f(A) uf(B) 2. If AC B, then…

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Q: Use the Product Rule to differentiate f(v) = v-4sinv

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Q: Exercise 5: If f(x) = x5 + 2x³ + 2x, check that f is injective and find (f-1)'(-5).

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Q: d dx y' z' y" z"

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Q: Determine whether the function f : R\{2} –>R\{0}, defined by f(x)=(1/(x-2)) is bijective or not.

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Q: Let f(x, y) = Evaluate f(5,5) 175 - 3x² - 4y2

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Q: 3. Let the function f :R →Rbe defined as follows: [3x–1 if x> 3 f (x)={x² – 2 if -2<x<3 2x+3 ifx<-2…

A: Given f(x) = 3x-1ifx&gt;3x2-2if-2≤x≤32x+3ifx&lt;-2

Q: (4xy) w = 3 sin (4xy tan (z) +4 In (5yz)- 8 e

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Q: (b) State the range of f for the domain given in part (a). f:A B f(x)=(x-1)²+4. (c) Define the set B…

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Q: fluu) is a function, fl13|=0 fal-1.31=2 ,fg(-1.3) =-3 glxiy.z)=f(xyz,xzyzz?) So Vg(1,-1,1)? %3D

A: Gradient of the function w=f(x,y,z)  is given by ∇f=∂f∂x,∂f∂y,∂f∂z Chain rule of derivative: Let us…

Q: Let F = (2xz+y², 2xy, x²+1), if Vf= F, find f(1, 1, 1) – f(0, 0, 0)

A: Given vector funtion and

Q: = Let p¹²-2x+1, p² = 3 +3x+1 and p35x + 10. Let = x³-3x + 4. Is q in me span of pl,p2 and p3?

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Q: Show that f(z) = 3z² + 2z+5 is analytic function.

A: Given

Q: Let f(x,y,z,w)=45x3z-1/y+wz3. Evaluate f(a,b,c,d) where a,b,c are non-zerol real numbers

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