6. Let R(ABCDEFGH) satisfy the following functional dependencies А В.CH A, B E, BD C. EG H. DE F. Which of the following FD's is also guaranteed to be satisfied by R? a) BFG AE ich or the rollowing FD'S is also guaranteed to be satisned by b) CGH BF c) ACG DH d) ADG CH
x+2 7 21. multiple choice. Any iten may! y have more than one correct answer. 2. what is the domain of f(x) = x²-3x-28 (10 m) (-2,-4) u (-4,-2) +(-2,7) v (7,) b) (-2,-4) u (-4,7) 0 (7,-) c) (-0, -u) u 17, s ) d) (-2,-2) u (-2,-) e) (-4,7) 22, 22, which equation can be used to find the equation of a line that passes through (2,-5) and is perpendicular to 2x + 3y = 7? (1 pt)...
Problem 1-4. Let AABC be a right triangle with hypotenuse AB. Suppose that D, E, F e AB, BF ZACB. Prove that ZDCE ZECF. FA, ZBDC is a right angle, and CE is the bisector of В E 14 F onu Rnonocitions 1.31 on these-but be sure to label what IT.
n+1 2. Let an = (-1)"-for n > 1. (a) What is sup(fas, ab,...])? (b) What is supa,)? (d) What is liminfan-sup ((inf((an.an+1, )) | n = 1,2.. ..))?
[1 1 0 1 5) (Inverses) Let A = 2 1 0 | 3 2 1 (a) Find A- using elementary row operations. (x+y-2 =0 2x + y - 5 = 0 3.0 + 2y +z=1. (b) Using the result found in (a), solve the system
4. Let A and B be n x n such that B = 1-A and A2 = A. Show that AB BA = 0 4. Let A and B be n x n such that B 1-A and A2 = A. Show that AB-BA-0 4. Let A and B be n x n such that B = 1-A and A2 = A. Show that AB BA = 0 4. Let A and B be n x n such that B...
Problem 4 Let lim an = A, lim bn = B. Show that limah = AB Proceed by following these steps. (a) Verify that | ab. - AB| = |a,(6,- B)+a,B - AB S 14,1-16,- B+B |a, -Al<e bounded small constant small Why is it possible to assume that "bounded times small + constant times small" is less than epsilon? (b) Let M be such that Jan <M Wn. Let Ni be such that 12x - Al <10+1 Yn >...
3 - 12 Let A = Construct a 2x2 matrix B such that AB is the zero matrix. Use two -4 16 different nonzero columns for B. B=
1. Let a and b be elements of a group . Prove that ab and ba have the same order. 2. Show by example that the product of elements of nite order in a group need not have nite order. What if the group is abelian?
Given the directed graph with vertices(A, B, C, D, E, F, G, H, I) Edges (AB=5, BF = 4, AC = 7, CD=3, EC = 4, DE = 5, EH = 2, HI = 4, GH = 10, GF = 3, IG = 3, BE = 2, HD= 7, EG= 9 1. What is the length of minimum spaning tree? 2. Which edges will not be included if we use Kruskal's algorithm to find minimum spaning tree?