4. T: R2 + R2 is a function such that T(1,1)= (1,0) and T(1, -1) =...
Let T: P2 --> R2 be the linear transformation such that T(x+1)=(1,1), T(x2)=(1,0) and T(x-1)=(0, 1). Find T(2+x+x2).
T:R3 → R2 is a linear transformation with T(1,0, 2) = (2, -1) and T(0,1, -1) = (5,2). It follows that T(2, -3, 7) is equal to Select one: 0 a. (7,1) O O b. not enough information is given to determine the answer C. (-11, –8) O d. (2, -3) o e. (19,-4)
T:R R2 is a linear transformation with T(1,0, 2) = (2, 1) and T(0,1,-1) = (-5,2). It follows that T(2, -3,7) is equal to Select one: 0 a. (-11, -8) O b. (2, 3) c (19, -1) d. not enough information is given to determine the answer e(-3,3)
Question 19: Linear Transformations Let S = {(u, v): 0 <u<1,0 <v<1} be the unit square and let RCR be the parallelogram with vertices (0,0), (2, 2), (3,-1), (5,1). a. Find a linear transformation T:R2 + R2 such that T(S) = R and T(1,0) = (2, 2). What is T(0, 1)? T(0,1): 2= y= b. Use the change of variables theorem to fill in the appropriate information: 1(4,)dA= S. ° Sºf(T(u, v)|Jac(T)| dudv JA JO A= c. If f(x, y)...
2. Suppose T is a linear transformation of R', and we know that T(1,1) =(2,0) and T(1,-1) = (0,2). What is 7(3, 4)? (Bonus 2 pts.) In problem (2), what is T(x, y)?
11. Suppose S: R R2 is the linear transformation with matrix -3 11 [2 -6 2 relative to the bases & and &. Find the matrix of S with respect to the bases (1,0, 1), (1,0,0), (1, 1,0)) and ((1,-1). (2,0). 11. Suppose S: R R2 is the linear transformation with matrix -3 11 [2 -6 2 relative to the bases & and &. Find the matrix of S with respect to the bases (1,0, 1), (1,0,0), (1, 1,0)) and...
1. Compute the following integrals: (a) S1 (x+y+2)dA where T C R2 is the triangle with vertices (-1, -1), (0, 2) and (1,1) (b) S(3x + 6y)<dA where D is the quadrilateral with vertices (0,1), (2,0), (0, -1) and (-2,0)
Consider the three points (-1,0), (0,1), (2,0) 1. Construct a second degree polynomial P(a) that interpolates the given points. Use Matlab to solve the resulting linear system. 2. Find a piecewise linear function L(x) that interpolates the given points. Consider the three points (-1,0), (0,1), (2,0) 1. Construct a second degree polynomial P(a) that interpolates the given points. Use Matlab to solve the resulting linear system. 2. Find a piecewise linear function L(x) that interpolates the given points.
DLM R A 2,3 -1,0 1,1 B -1,3 3,0 2,1 C 0,0 0,10 3,1 D 4,3 2,0 3,1 Part a: What are the pure strategies that are strictly dominated in the above game? Part 6: What are the rationalizable strategies for each player? What are all the rationalizable strategy profiles? Part c: Find all of the Nash equilibria of the game above.
1. Compute the following integrals: 9 (a) S (x+y+2)dA where T C R2 is the triangle with vertices (-1,-1), (0, 2) and (1,1) (b) Sp (3x + 6y)<dA where D is the quadrilateral with vertices (0,1), (2,0), (0, -1) and (-2,0) 2 9