Let u = (-3, 2), v (0,-1) and A = %D %3D %3D NOTE: Give ezact answers. (a) Find ||u|| relative to the inner product on R generated by the matrix A. u|= /34 (b) Find d(u, v) relative to the inner product on R generated by the matrix A. d(u, v) -29 %3D
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- So i calculated the LU decomposition of a matrice. (as seen in picture) How do I use the LU decomposition to solve : 2x+2y+z = 1 6x+5y+5z=3 -4x-5y+5z=-7 Thanbk you in advanceWhich does NOT describe a way to map this square back onto itself? A) A reflection in the x-axis B) A 90° counterclockwise rotation about (-2, 0) C) A 270° counterclockwise rotation about the origin D) A reflection in x = -2A median of a triangle is a segment connecting a vertex of a triangle to the midpoint of the opposite side. Let T be the triangle with vertices (0, 0), (a, 0), and (c, d). Prove that the centroid of triangle T is two-thirds of the way from each vertex to the opposite side.
- Find the norm of (-4,- 1/4,3, 1/3) belong to R^4 w.r.t the Euclidean Inner Product on R^4.Solve the system u=2x−y, v=x+3y for x and y in terms of u and v. Then find the value of the Jacobian ∂(x,y)∂(u,v). Find the image under the transformation of the triangular region with vertices (0,0), (3,6), and (3,−1) in the xy-plane. Sketch the transformed region in the uv-plane.use gaussian and gauss jordan elimination or LU-decomposition no.2 only
- Check whether the following inner product <, > defined by <alpha,beta>=x1y1 + 2x1Y2 + 2x2y1 +5x2y2, where a = (x1,x2) and B = (y1,y2) is an inner product in R or not? Justify your answer. Image of question attached.a. Solve the system u = 3x + 2y, y = x + 4y for x and y in terms of u and y. Then find the value of the Jacobian ∂(x, y)/∂(u, y). b. Find the image under the transformation u = 3x + 2y, y = x + 4y of the triangular region in the xy-plane bounded by the x-axis, the y-axis, and the line x + y = 1. Sketch the transformed region in the uy-plane.. Solve the system u=2x+3y, v=x+4y for x and y in terms of u and v. Then find the value of the Jacobian ∂(x,y)∂(u,v). b. Find the image under the transformation u=2x+3y, v=x+4y of the triangular region in the xy-plane bounded by the x-axis, the y-axis, and the line x+y=1. Sketch the transformed image in the uv-plane. Question content area bottom Part 1 a. x=enter your response here, y=enter your response here Part 2 The Jacobian is enter your response here. Part 3 b. Choose the correct sketch of the transformed region in the uv-plane below.
- 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^2Explain why fitting a conic through the points P1(x1, y1), . . . , Pm(xm, ym) amounts to finding the kernel of an m × 6 matrix A. Give the entries of the ith row of A. Note that a one-dimensional subspace of the kernel of A defines a unique conic, since the equations f (x, y) = 0 and k f (x, y) = 0 describe the same conic.Find (a) ⟨u, v⟩, (b) ||u||, (c) ||v||, and (d) d(u, v) for the given inner product defined on Rn.u = (1, −1, 2, 0), v = (2, 1, 0, −1), ⟨u, v⟩ = u ∙ v