+ b3 + c3 – 3abc for Problem 1.16 Find all integers that can be represented...
Problem 2. Find (with proof) all positive integers n that have an odd number of positive divisors (for example 6 has 4 positive divisors 1,2,3,6).
The product of two consecutive integers is 42. Find all such pairs of integers. The positive set of integers: x = and x+1 = The negative set of integers: x = and x+1 =
P7.16. What range of decimal integers can be represented by a. three-bit binary numbers; b. three-digit octal numbers; c. three-digit hexadecimal numbers?
Assume that the transition matrix from basis B = {b1, b2, b3} to basis C = {c1, c2, c3} is PC,B = 1/2*[ 0 -1 1 ; -1 1 1 ; 1 0 0 ]. (a) If u = b1 + b2 + 2b3, find [u]C. (b) Calculate PB,C. (c) Suppose that c1 = (1, 2, 3), c2 = (1, 2, 0), c3 = (1, 0, 0) and let S be the standard basis for R 3 . (i) Find...
please show all steps Find the new coordinate vector for the vector x after performing the specified change of basis. 8) Consider two bases B = 61, 62, 63 and C = C1, C2, C3) for a vector space V such that b1 = C1 + 2c3, b2 = C1 + 4c2 - C3, and b3 = 301 - C2. Suppose x = 51 +6b2 + b3. That is, 8) suppose [x]8 = 6 . Find [x]c A) B)
Problem 4. Determine if the following sets B1, B2, B3, B4 and Bs are open, closed, compact or connected. (You don't need to prove your findings here) a) B1 =RQ. b) We define the set B2 iteratively: C1 = [0, 1] C2 =[0,1/4] U [3/4, 1] C3 =[0,1/16] U [3/16, 4/16] U [12/16, 13/16] U [15/16, 1] Then B2 = n Cn. NEN c) B3 = U (2-7,3+"). nn +1 NEN d) f:R+R continuous and V CR closed. B4 =...
AUTOMATA THEORY 1 using G=({A, B3, {a,b, c3, A, p) P: A al aca Al abBC - B - abb Alb And using Ĝ= ({A,B}, {a,b,c}, A, p) P: A al aaAl ababb Acl abbc 3-7 abb Alb show a derivation tree for the string ababbac, using both grammars provided above.
Given n bits, how many unsigned integers can be represented with the n bits? What is the range of these integers? (6 points) There are 26 characters in the alphabet we use for writing English. What is the least number of bits needed to give each character a unique bit pattern? How many bits would we need to distinguish between upper- and lowercase versions of all 26 characters? (12 points)
select all that apply please Q&/3) = {a + b3 + c^9: a,b,c € Q} QUESTION 4 Which of the following rings R. is S a subring of R? O R = set of integers, S = set of odd integers. OR is the set of integers, and S = 6Z R is the set of complex numbers, and 5 = {a + bi: a, b E ZH R= Z125Z, and S = {0,5,10,15,20). QUESTION 5 Which of the following...
8. Consider the following algorithm, which finds the sum of all of the integers in a list procedure sum(n: positive integer, a1, a2,..., an : integers) for i: 1 to n return S (a) Suppose the value for n is 4 and the elements of the list are 3, 5,-2,4. List assigned to s as the procedure is executed. (You can list the the values that are values assigned to all variables if you wish) b) When a list of...