answer number 6,7,8 1 For Problems 1 through 8: Find the following polynomials Irro(a,x). Hint: Set...
Question 4: 4. Show that the following polynomials form a basis for P3 1 - x, 1-x2 1 +x _X 5. Show that the following matrices form a basis for M22 -8 1 0 3 12 -6 -4 2 _ 13. Find the coordinate vector of v relative to the basis S = {v1, V2, V3} for R3 (a) v (2, -1 3); vi = (1,0, 0), v2 = (2, 2, 0) Vз — (3, 3, 3) (b) v (5,...
QUESTION 1 Let V-L2([0,1 ],C) and > : Vx-СУч . Г f(x)g(x)dx be an inner product on V Let gor 91, 92, 93:0,1]R be given by gox)-1,g1(x)-x, 920x)-x2, g3(x) -x3 and consider the following subset S = { go, g 1, g 2, g3JC V. After applying the Gram-Schmidt process the following set of vectors T = {vo, vľ, V2, V3} is an orthonormal set, where V1, V2, V3, and V4 are given by: O vo= 1, v,-V3(2x-1), v,-V5 (6x2-6x...
(1) Let u = (-1,2) and v = (3, 1). (a) (5] Find graphically the vector w = (2u - v). (b) (5] Find algebraically the vector z=3u - 2 (2) (a) [5] Write u ='(1, -5, -1) as a linear combination of v1 = (1,2,0), v2 = (0,1,-1), V3 = (2,1,1). (b) (5] Are the 4 vectors u, V1, V2, V3 linearly independent? Explain your answer. (C) (5) Are the 2 vectors V, V3 linearly independent? Explain your answer....
1. Let Q be the set of polynomials with rational coefficients. You may assume that this is an abelian group under addition. Consider the function Ql] Q[x] given by p(px)) = p'(x), where we are taking the derivative. Show that is a group homomorphism. Determine the kernel of 2. Let G and H be groups. Show that (G x H)/G is isomorphic to H. Hint: consider defining a surjective homomorphism p : Gx HH with kernel G. Then apply the...
PART 2: Assorted Problems. Show all work for full credit. (8) 1. In each of the following, determine whether or not the subset W of the vector space Vis a subspace of V. Justify your conclusions. a. V-Mn: W the set of all 2x2 matrices with rational number entrics b. VP: W-the set of all polynomials a, +ar+a in where a, +a, -2a, -o. (b) 2. Find elementary matrices E,E, such that EA-B and E,B-A when 2 7 3 8...
Please answer A and B
1. Consider the following adjacency matrix representing vertices v through v^: weighted graph containing a ro 5 0 0 8 0 61 5 0 0 7 0 0 0 jo 0 0 0 0 1 3| 0 7 0 0 2 0 0 8 0 0 0 0 1 0 0 0 4 L6 0 3 0 0 4 0- 20 0 0 a. Draw the graph resulting from the adjacency matrix b. Assuming the...
1. Find A if (2A)' = [ : :] 2. Determine if {(x,y) : x - y = 1) is a subspace of vector space V - R 3. Let vi, V2, V3 be three linearly independent vectors in a vector space V. Is the set {v1 - 2v2, 2v2 - 3v3, 3V3 - Vi} linearly independent or linearly dependent? Prove your answer.
this is Theron 13 -8
EXERCISES 1. Prove that § (-1)"qn = 1 619"). (Hint: Set z=-1 in Theorem 13-8.] 1- qn (1-9 -). (Hint: Set z=g 2. Prove that in Theorem 13-8.] I (1 qa**) (1 + zqn+) (1 + x**q+1) = 1 - 9² n+2) (1 + zq2n+1) (1 + 2-10 3 qu*z". (132-12) an n. (13-2-12) 72 = 0 n= -00
7. Find cov(X, Y)
8. Are the random variables X, Y independent? Justify
answer
Edit : do not solve number 1, I already solved.
C=3/32
Use this information for problems 1 -8: Let X, Y be two continuous random variables and let f(x, y)2y + xy?) over the range O< x<2 and 0< y< 2. Determine the v function alue of the constant c that makes this function a joint probability density 1.
Use this information for problems 1 -8:...
1. Find the solution set for each of the following on the interval - 27 x < 2 A. secx = 2 B. 5 sino - 3 = sin - 5 C. 3tan? = 1 D. sinr = cos E sin cos 7 = r = - sin 2. Find the solution set for each of the following on the interval 0 <r <2 A. COSI = cos x B. 2 sinr = sin C. 2 sinx: - sin x...