7. Determine whether (u,v) =3u, v, – 2u, v, is a valid inner-product function or not for R²

Q: Determine a scalar s such that A2x = sx when Ax = rx.

A: To determine a scalar s such that A2x=sx when Ax=rx Given Ax=rx On multiplying both the sides by…

Q: Find the sum of product expansion of the function F(x, у, 2) 3D (х + у)xz + хух + у z хух + хух + ху…

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Q: Show that the function u(z, t) : satisfies ua = %3D %3D a2t2-2

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Q: Show that the function does not define an inner product on R3, where u = (u1, u2) and v = (v1, v2).…

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Q: Show that the function a Y1 (x, y) = [21 2] в с Y2 is an inner product on R? if and only if b2 – ac…

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Q: Let f be a function defined in R2 by f(x,y) = 3x2 - 2x3 - 3y2 + 6xy.  Find the gradient vector in…

A: We have to solve given problem:

Q: Find div F and curl F if F(x,y,z) = x³i - 6j+yzk.

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Q: please solve this linear algebra problem.

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Q: 3. Show that every y E lị defines a continuous linear functional on l through the inner product,…

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Q: show that the scalar t that minimizes ||y– tx||

A: In this question, we need to find the t that minimizes ||y-tx||.

Q: 9. Show that the function (-, -) : IR² × R² → IR defined by setting = #1#2 + 2x12 + 2y1*2 + 8y1Y2 /2…

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Q: Enter the function In standard form. y = 2(x-1)(x +5) The standard fom of y = 2(x-1)(x +5) is

A: y=2(x-1)(x+5) first multiply (x-1)(x+5) =>(x-1)(x+5) =>(x^2 +5x -x -5) =>(x^2 +4x-5)

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: Let f(x) = 3x² and. P = {–2, –1, 0, 1, 2, 3}. Compute Lf(P) and U,(P). %3D %3D

A: Consider: fx=3x2 and P=-2,-1,0,1,2,3. Compute LfP and UfP.   If P is a partition such that…

Q: Find the work done by the force F = x²yi– xy²j along the paths shown from (1, 1) to (4, 2). (4, 2) a…

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Q: [2] Show that the functions f (x) = 4x" , and f,(x) = x*+* linearly independent (-00, 00). are on

A: To Show: Show that the functions f1x = 4xn, and f2x = xn+4 are linearly independent on -∞, ∞…

Q: Compute (S ,g) where f(t)=1– 3r² , g(1)=t-ť'onV = C[0,1]. %3D

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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: Suppose F (x, y) = (2xe-", 2y – a²e="} (a) Find a scalar function f (x, y) such that F = Vf (b) Use…

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Q: Evaluate O F.dT where +(3y %3D y + 1 and C is the triangle with vertices: (0,0), (6,0), (3, 5).

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Q: Justify that (•, ·) defines an inner product on R?. the function (', ·) defined on R? as follows: U1…

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Q: Evaluate the work done between the points P, (3,1,4) and P, (6,3,6) for the conservative field F =…

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Q: Show that the function f(x, y, 2) = (x² + y² + 2e**)4 is strictly convex on R³.

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Q: Let F1 = (x+ y)Âx + (-x+y) ŷ– 2zî and F2 = 2 yx+ (2x +3z) ŷ +3yî. Calculate the curl and divergence…

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Q: Let f(x, y) = x² + In(2x – y). Find the gradient Vf(x, y) at the point (1, 1). O O O O

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Q: The gradient vector of the function f defined by f(x,y)= In(1+7x² +5y²) is equal to Select one: O…

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Q: #Let Vz arih Here, れgl。 and hahe what netationship must hold betaen adho foro v to be ewoatly…

A: The expression for the volume is V=πr2h.   Thus, the total differential is given by dV=∂V∂rdr…

Q: 4. Let f(x, y) be a function defined on a disk D not containing the origin which is given by 2.x2 f…

A: as per our company guideline we are supposed to answer only one qs kindly post remaining qs in next…

Q: use the inner product = p(x)q(x)dx. to find the projection of p(x) q(x) = 5x + 2. = S'; x3 onto

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Q: Let f(x,y,z) = x² e Vy*+ Compute f(3, - 5,3) and f(5,8, - 6).

A: Given that     f(x,y,z) = x2 e√(y^2+z^2)

Q: Show that the function does not define an inner product on R3, where u = (u1, u2, u3) and v = (v1,…

A: For satisfying the inner product condition, function has to follow these three conditions: 1)…

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: 10. Show that 1/x, x are linearly independent on (0, 0).

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Q: Show that the function defines an inner product on R3, where u = (u1, u2, u3) and v = (v1, v2, v3).…

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Q: Let C[0, 1] have inner product [f(x), g(x)] = ∫ f(x)g(x) dx. Find α so that (x + αx2 ) ⊥ (x + 1)

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Q: Consider P2 with the inner product = f (x)g(x) dr. Then d(x, 2) Jo

A: d(x,2) represents distance between the vectors x and 2 P2 is the set of all polynomials with degree…

Q: Show that the function does not define an inner product on R3, where u = (u1, u2, u3) and v = (v1,…

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Q: Show that the function defines an inner product on R3, where u = (u1, u2, u3) and v = (v1, v2,…

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Q: Use Green's Theorem to evaluate F dr, where F(2, y) = (9xy, y" - 8) and C is the rectangle with…

A: That's easy. Have a great day!!!

Q: 4. If A andB are differentiable functions of a scalar u, prove that (А В) — А В du d (a) dA B du du…

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Q: 19: Find two linear operator T, and T,on V(R) such that T,T, = 0 but T,7, - 0.

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Q: Let r; = ro + hj for j = 0,1,2. Use the quadratic polynomial interpolating f at those nodes %3D %3D…

A: The solution is given below

Q: Find the Jacobian of following functions f(x,y, z) = 3xy – yz + 2y z2 - 5xyz3 g(x,y, z) = xyz -…

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Q: Find the Wronskian for the set of functions.{1, x, x2, x3}

A: we have to find the wronskian for the set of functions. {1, x, x2, x3}

Q: Show that the function defines an inner product on R2, where u = (u1, u2) and v = (v1, v2). ⟨u, v⟩ =…

A: Given function u,v=u1v1+9u2v2 where u=u1,u2 and v=v1,v2 The function is defined on R2. To show that…

Q: The inner-product function satisfies : Select one: O a. = O b. = O c. = 0 O d. is greater…

A: We will use the definition of inner product function.

Q: 6. Let f(u, v) = u sin(v) – v cos(u) and u(r,y) = r² – ry² v(r, y) = y – r Find af af and both by…

A: We need to find the derivatives using direct substitution and by chain rule . Now , we have ,…