- Consider the polytope P = Conv((1,1, -1), (1, -1, -1),(-1,1, -1),(-1,-1,-1), (0,0,1)) Represent P as...
Can someone please help? Question 2. Let B = {(1,-1,1),(-1,1,1)} and C = {(1,-1,0),(0,0,1)} be subsets of R3 (a) Show that both the sets B and C are linearly independent sets of vectors with span B = spanc (12 marks] (b) Assuming the usual left to right ordering, find the transition matrix PB- [2 marks] (c) Given a basis D of R?, find the transition matrix PB-D given Pc+b = (32) [3 marks (d) Use the transition matrix PC-D in...
Are the points P = (0,0,−1), Q = (0,1,0) and R = (0,0,1) collinear ?
Exercise 23. Let φ(z) = z/(1-Iz) for all E (-1,1). (a) Show that p is a bijection from (-1,1) to R. (b) Find φ-1, (By a suitable use of lul, write your answer in the form of a single formula.) Hint: Combine the results of Exercise 20 and part (c) of Exercise 22.)
CHANGING COORDINATES/BASIS Question 1. Let R be the triangle in R2 with vertices at (0,0), (-1,1), and (1,1). Consider the following integral: 4(x y)e- dA. R Choose a substitution to new coordinates u and v that will simplify this integrand. Draw a sketch of both the region R and the image of the region in the u,v-plane. Evaluate the integral in the new coordinate system. Warning: No matter what strategy you use for this integral, it will require at least...
Question 1) (3 Points) Consider the strong form below. Derive the weak form equation. The space used is W H-1,1]. Define the spaces Wp and Wo Dirichlet Strong Form: Find u e W2,00 such that u"(x) _ 2 sin(x)a(z) u(-1)-1 u(1) 1 cos(x), for any x ? ?-[-1,1]
Consider the following game: Player 1 announces an integer p in the interval (1.201. Player 2 then announces an integer g in the interval (21.40) . Ifp-1, then the game is a tie (each player gets a payoff of zero). . If q is prime, then Player 1 wins (the payoffs are (1,-1). . If pand q have a common factor greater than 1, then Player 1 wins (the payoffs are (1,-1). If pand qare relatively prime (but g is...
Please help solve the following with steps. Thank you! 2. Determine the center of mass of each region below given the variable density (a) The square with vertices (0, 0), (0,1), (1,1), and (1,0) with ρ(x,y) = 1 + 0.5x (b) The uper half of the disk of radius 4 with p(x, y) 12 y2. 2. Determine the center of mass of each region below given the variable density (a) The square with vertices (0, 0), (0,1), (1,1), and (1,0)...
2. Let A:(-1,1,-1), B:(2,0.2), C:(4.1.-3), and D:(-3, 1, 10) be points in R. (a) Find the angles (in degrees) of the triangle with vertices A, B and C. (b) Find an equation of the plane passing through the points A, B, and C. (c) Find two unit vectors perpendicular the plane through A, B, and C. (d) Find the volume of the tetrahedron with vertices A, B, C, D. 3. (a) Find an equation of the tangent line to the...
Consider polynomial interpolation of the function f(x)=1/(1+25x^2) on the interval [-1,1] by (1) an interpolating polynomial determined by m equidistant interpolation points, (2) an interpolating polynomial determined by interpolation at the m zeros of the Chebyshev polynomial T_m(x), and (3) by interpolating by cubic splines instead of by a polynomial. Estimate the approximation error by evaluation max_i |f(z_i)-p(z_i)| for many points z_i on [-1,1]. For instance, you could use 10m points z_i. The cubic spline interpolant can be determined in...
PlayerI C D E A 0,0 0,2 2,1 В 1,2 1,1 0,0 Player B Consider the game in strategic form above. If player 1 plays A and player 2 plays E, Player 1's payoff is a. Impossible to determine. b. 2 C. d. 0)