Use the defınition of an inner product to determine which of the following defines an inner producton the indicated space. Verify your answers.vịa. (u, v) = u1vị – Uzvl – u1v2 + 3u2v2 for u =and v =U2in R?V2b. (f, g) = f'(0)/(0) for f,g € D(-1,1) (where D(a, b) is the vector space of all differentiiblefunctions on the interval (a, b))c. (u, v) = (Au)(Av) for u, v E R" and A is invertible n x n matrix.

for a real vector space, an inner product satisfies the following four properties. Let , , and be…

Answered: Use the definition of an inner product…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 12T

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Similar questions

Integrate G(x, y, z) = y + z over the surface of the wedge in the first octant bounded by the coordinate planes and the planes x = 2 and y + z = 1.
Integrate G(x, y, z) = xyz over the surface of the cube cut from the first octant by the planes x = 1, y = 1, and z = 1
Two surfaces S and S^(-) with a common point p have contact order ≥ 2 at p if there exist parametrization x(u,v) and x^(-)(u,v) in p of S and S^(-) respectively such that xu = x^(-)u, xv = x^(-)v, xuu = x^(-)uu, xuv = x^(-)uv, xvv = x^(-)vv at p. Prove the following: a. Let S and S^(-) have contact order greater than or equal to 2 at p; x:U -> S and x^(-): U -> S^(-) be arbitrary parametrizations in p of S and S^(-) respectively and f: V c R^(3) -> R be a differentiable function in a neighborhood V of p in R^(3). Then the partial derivatives of order smaller than or equal to 2 of f o x^(-): U -> R are zero in x bar^(-1)(p) iff the partial derivatives of order smaller than or equal to 2 of f o x: U -> R are zero in x^(-1) (p). b. Let S and S^(-) have contact of order smaller than or equal to 2 at p. Let z = f(x, y), z = f^(-) (x, y) be the equations in a neighborhood of p, of S and S^(-) respectively where the xy plane is the common tangent plane at p = (0, 0). Then the…
Let X=(x1,x2) and Y==(y1,y2) belongs to R^2. Verify that<X, Y> = 5(5x2y2+ x1y1-2x1y2-2x2y1) is an inner product on R^2
C is the hexagon in the xy-plane with vertices (5, −5), (5, 5), (0, 10), (−5, 5), (−5, −5), and (0, −10), directed counter-clockwise. Evaluate integralC (3y/(x^2+y^2) dx − 3x/(x^ 2 + y^2) dy)
find ⌠⌠F*dS if F(x,y,z)=2xi+2yj+2zk and S is the paraboloid z=8-x^2-y^2 lying above the rectangle [0,1] x [0,2] and has upward orientation
In V=R3 Let W1 be the xy-plane and let W2 be the z-zxis: W1={(x,y,0):x,y∈R} and W2={(0,0,z):z∈R} Show that

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