ww-{) [:]}------ Let W =Span 2 1. and suppose the vectory is in W . Find...
Suppose X Gamma (a; b) and YGamma (c; d). Let W-X+Y. (a) Find the MGF of w. (b) What restrictions would need to be placed on the values of a, b; c; and d for Ww to be a Gamma Random Variable. What would the parameters be?
Let V = M2(R), and let U be the span of S = 2. (a) Let V = M,(R), and let U be the span of s={(1 1) ($ 3). (3), (1 9). (1) 2.)} Find a basis for U contained in S. (b) Let W be the subspace of P spanned by T = {2} + 22 – 1, -2.3 + 2x +1,23 +22² + 2x – 1, 2x3 + x2 +1 -2, 4.23 + 2x2 - -4}. Find...
2. (4) Let W = span{(1,1,1), (-1,1,0)). Let v = (1,-1,2). Find the decomposition v = w; + W2, where we W and W, EW+.
Let W Span((2,-3,0, 1), (4,-6,-2, 1), (6,-9,-2,2) R4. (a) Find a basis for W (b) Find a basis for W (c) Find an orthogonal basis for W and W (d) The union of these two orthogonal bases (put the basis for W and W what? Why is the union orthogonal? into one set) is an orthogonal basis for Let W Span((2,-3,0, 1), (4,-6,-2, 1), (6,-9,-2,2) R4. (a) Find a basis for W (b) Find a basis for W (c) Find...
1. Let 1 -1][-1 s={ 112 [1] 1 1 Find a basis for the subspace W = span S of M22. What is the dim W? 2. Find the basis for the solution space of the homogeneous system: a. x+2y = 0 2x+4y =0 b. 3x+2y+4z=0 2x+ y - Z = 0 x +y +3z =0
Consider the subspaces U=span{[4 −2 −2],[10 1− 4]} and W=span{[3 −4 −1],[10 2 −2]}.Find a matrix X∈V such that U∩W=span{W}.
20 3. Let 1 = 2 and = 5. Let W = Span{11, 13). (a) Give a geometric description of W. (b) Use the Gram-Schmidt process to find an orthogonal basis for W. (c) Let = 2 Find the closest point to į in W. (a) Use your orthogonal basis in part (b) to find an orthonormal basis for W.
Let W = Span -1 3 10 Find Wt in R4.
Let W = span{ (-2, 1; 2,0), (4,0-5, 2)] the Groun - Student Produrt to find an enthonormal basis for W The dimension of wt, the orthogonal complement of w.is basis from (a), either before or after normalizing projw (1,1,1,). be your to find
1. Let the production function be y = c. (a) Suppose the price of is w = 1. Find the firm's total cost curve C(y), average cost curve AC(y), and marginal cost curve MC(y). (b) Assume that p> min AC(y), find the firm's supply curve y(w,p). (c) Suppose the price of y is p = 10, and the price of the input r is w = 1, calculate the firm's profit. 2. Assume the production function is y = 5.3...