fi(x) 1 A = {fi, f2, f3} c F(R) and f(x) = f:(x) = |x+ 1| PROVE: A is linearly independent. (A L.I.)

Q: The functions f(r) 4t2 and g(r) = 3t|t| are linearly independent on (-oo, 0) %3D Select one: O True…

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Q: 4 3 2 1 y 1 y = f(x) 2 3 4 -X

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Q: If f(x) = x + /2 – x and g(u) = u + v2 – u , is it true that f = g?

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Q: If f(x, y) = In (2x-3y), then find of ||

A: We can solve this problem using partial derivatives.

Q: Let the invertible function Evaluate f(x) = 3x³+x+3 1 = ["] † ^¹ (2²) dar dx (Hint: You may use the…

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Q: 3. (b) Consider the function f(x, y) = a(x² + y²) + xy + 1 for some real number a. Find Vf. Find fxx…

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Q: Find div F if F(x, y, z) = (x2 + y) i + z2 j + (ey - z) k.           A . 2xy i + k          B. 2x…

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Q: xercise II.2. let F(): R² R³ and G(): R² R² be given by (fi(x)) f2(x) f3(x)) F(x) = (iii) f3 and ere…

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Q: 2. Let f= L(X,Y). Show that ƒ is one to one iff (f(x).(x)....(x)) is linear independent when (x,x)…

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Q: fi(x) A = {fi, f2, f3} c F(R) and f(x) fa(x) 1 |x+ 1| PROVE: A is linearly independent. (A L.I.)

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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: Find the linearization of the function f(p, q) = Pat (0,0) p-1 q+1

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Q: Determined whether the given function is linearly independent or dependent on (-00, c0) f.(x) = x,…

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Q: Consider the functions f, g given by f(y) = Ay, g(x) = Bx where A is m × p and B is p × n. In…

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Q: 5) Find functions f and g so that f • g = H -3 H(x) = Vх — 2

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Q: Are the functions f, g, and h given below linearly independent? f(x) = et – cos(5æ), g(x) = e* +…

A: The functions are linearly dependent :

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