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mathematics
survey of mathematics

Questions and Answers of Survey of Mathematics

Consider the mathematical system(a) What is the binary operation?(b) Is this system closed? Explain.(c) Is there an identity element for this system under the given operation? Explain. (d) What
Is clock 5 arithmetic under the operation of addition a commutative group? Assume that the associative property holds. Explain your answer.
Develop a clock 5 arithmetic addition table.
Is the set of natural numbers a commutative group under the operation of subtraction? Explain your answer.
Is the set of integers a commutative group under the operation of addition? Explain your answer.
List the requirements needed for a mathematical system to be a commutative group.
What is a mathematical system?
Given and determine the following.B x A -1 A = 0. -3 [3 B = 5 2]
Given and determine the following.A x B -1 A = 0. -3 [3 B = 5 2]
Given and determine the following.3A - 2B -1 A = 0. -3 [3 B = 5 2]
Given and determine the following.A - B -1 A = 0. -3 [3 B = 5 2]
Given and determine the following.A + B -1 A = 0. -3 [3 B = 5 2]
Julie, a police officer, has the following work pattern. She works 3 days, has 4 days off, then works 4 days, then has 3 days off, and then the pat-tern repeats. Assume that today is the first day of
Construct a modulo 4 multiplication table. Then determine whether the modulo 4 system forms a commutative group under the operation of multiplication.
Construct a modulo 6 addition table. Then determine whether the modulo 6 system forms a commutative group under the operation of addition.
Determine all positive number replacements (less than the modulus) for the question mark that make the statement true.7 • ? ≡ 2 (mod 9)
Determine all positive number replacements (less than the modulus) for the question mark that make the statement true.? • 3 ≡ 5 (mod 6)
Determine all positive number replacements (less than the modulus) for the question mark that make the statement true.? • 7 ≡ 3 (mod 10)
Determine all positive number replacements (less than the modulus) for the question mark that make the statement true.10 • 7 ≡ ? (mod 11)
Determine all positive number replacements (less than the modulus) for the question mark that make the statement true.? • 4 ≡ 0 (mod 8)
Determine all positive number replacements (less than the modulus) for the question mark that make the statement true.7 • ? ≡ 5 (mod 8)
Determine all positive number replacements (less than the modulus) for the question mark that make the statement true.2 - ? ≡ 3 (mod 7)
Determine all positive number replacements (less than the modulus) for the question mark that make the statement true.2 + 5 ≡ ? (mod 6)
Find the modulo class to which the number belongs for the indicated modulo system.54, mod 14
Find the modulo class to which the number belongs for the indicated modulo system.71, mod 12
Find the modulo class to which the number belongs for the indicated modulo system.68, mod 8
Find the modulo class to which the number belongs for the indicated modulo system.56, mod 9
Find the modulo class to which the number belongs for the indicated modulo system.32, mod 8
Find the modulo class to which the number belongs for the indicated modulo system.23, mod 6
Consider the following mathematical system. Assume the associative property holds for the given operation.(a) What are the elements of the set in this mathematical system?(b) What is the binary
For the given mathematical system, determine which of the five properties of a commutative group do not hold. ! Δ ! ! !
For the given mathematical system, determine which of the five properties of a commutative group do not hold. P 4 4 4 4 4
For the given mathematical system, determine which of the five properties of a commutative group do not hold. зь аз 6 з а а зь аьз
Determine whether the set of rational numbers under the operation of multiplication forms a group.Explain your answer.
Determine whether the set of natural numbers under the operation of addition forms a group.Explain your answer.
Determine whether the set of integers under the operation of multiplication forms a group.Explain your answer.
Determine whether the set of integers under the operation of addition forms a group.Explain your answer.
List the properties of a group and explain what each property means
Determine the sum or difference in clock 12 arithmetic.7 - 4 + 6
Determine the sum or difference in clock 12 arithmetic.3 - 6
Determine the sum or difference in clock 12 arithmetic.11 + 9
Determine the sum or difference in clock 12 arithmetic.10 + 7
Is the set of real numbers closed under the operation of subtraction? Explain.
Is the set of whole numbers closed under the operation of division? Explain.
List the parts of a mathematical system.
What is a binary operation?
Two 2 x 2 matrices, A and B, whose product is the multiplicative identity matrix are said to be multiplicative inverses. That is, if A x B = B x A = I, then A and B are multiplicative inverses. In
For 2 x 2 matrices, the multiplicative identity matrix is . Show, for any 2 x 2 matrix, that A x I = I x A = A. I = a A = d]
Create three 2 x 2 matrices, A, B, and C, and show that (A x B) x C = A x (B x C).
Create three matrices, A, B, and C, with the same dimensions and show that (A + B) + C = A + (B + C).
Create two matrices, A and B, with the same dimensions and show that A + B = B + A.
Consider the mathematical system consisting of the set of all 2 x 4 matrices under the operation of matrix addition.(a) Is the system closed?(b) Is there an additive identity matrix? If so, what is
Consider the mathematical system consisting of the set of all 3 x 2 matrices under the operation of matrix addition. (a) Is the system closed? (b) Is there an additive identity matrix? If
To raise money for a local charity, the Spanish Club at Montclair High School sold hot dogs, soft drinks, and candy bars for 3 days in the student lounge. The sales for the 3 days are summarized in
Use matrix multiplication to determine the cost, in dollars, under the two purchase options (small and large quantities) to fill the day’s order.The Original Cookie Factory bakes and sells four
(a) Express these orders as a 1 x 4 matrix.(b) Use matrix multiplication to determine the amount of each ingredient needed to fill the day’s order.The Original Cookie Factory bakes and sells four
The Original Cookie Factory bakes and sells four types of cookies: chocolate chip, sugar, molasses, and peanut butter. Matrix A indicates the number of units of various ingredients used in baking a
Hollister sells two types of t-shirts—male and female. Matrix A indicates the stock on hand of each type and size of t-shirt at the beginning of a given day. Matrix B indicates the stock on hand of
Bakersfield High School sold tickets for the musical Grease. Matrix A indicates the number of student, adult, and senior citizen tickets sold for the matinee and evening shows on day 1. Matrix B
Show that the associative property of multiplication, (A x B) x C =A x (B x C), holds for matrices A, B, and C. 3 4 0. B = 2. 0] -2 3 3. ||
Show that the associative property of multiplication, (A x B) x C =A x (B x C), holds for matrices A, B, and C. 4 3] 4 C = B = -9- -2 I|
Show that the associative property of multiplication, (A x B) x C =A x (B x C), holds for matrices A, B, and C. 4 -2 4] 3 3 4 B = |-2 5. 5.
Show that the associative property of multiplication, (A x B) x C =A x (B x C), holds for matrices A, B, and C. 3 C = [ 3 B = 4 0 1 ||
Determine whether the commutative property of multiplication, A x B = B x A, holds for matrices A and B. -1 3 B = 3 -3
Determine whether the commutative property of multiplication, A x B = B x A, holds for matrices A and B. B = [ 8 -4 4 ||
Determine whether the commutative property of multiplication, A x B = B x A, holds for matrices A and B. 4 4 B = -3 -3 ||
Determine whether the commutative property of multiplication, A x B = B x A, holds for matrices A and B. -2 -3 -1 B = 4 -3. 4
Show that the associative property of addition, (A + B) + C = A + (B + C), holds for matrices A, B, and C. A = 4 B = 6 4 -5 -3 2] -11 c = : -5 ||
Show that the associative property of addition, (A + B) + C = A + (B + C), holds for matrices A, B, and C. 3 4 8 C =| 1 B = 4 -6 -6 9. -4 3.
Show that the associative property of addition, (A + B) + C = A + (B + C), holds for matrices A, B, and C. c=[| -2 B = 5 0] -2
Show the commutative property of addition, A + B = B + A, holds for matrices A and B. 4 -2 4 -2 -7 -11 2 -5 10 B = -1 -3 1 -4 2.
Show the commutative property of addition, A + B = B + A, holds for matrices A and B. 1 B = -4
Show the commutative property of addition, A + B = B + A, holds for matrices A and B. 2 0 6] 2 в-[-3 A = B =
Show the commutative property of addition, A + B = B + A, holds for matrices A and B. 4 B = 6.
Determine A + B and A x B. If an operation cannot be performed, explain why. 4 9. 3 A 3=
Determine A + B and A x B. If an operation cannot be performed, explain why. 5 А 3D[3 4], в %3 9. B = -8
Determine A + B and A x B. If an operation cannot be performed, explain why. Г1 2 B = [3 2. 4,
Determine A + B and A x B. If an operation cannot be performed, explain why. 3 2 5 3 4 B = A -2
Determine A + B and A x B. If an operation cannot be performed, explain why. 4 3 3 B = | 4 1 1 3.
Determine A + B and A x B. If an operation cannot be performed, explain why. 3 3 -2 [1 [7 B = [2 4 -1
Determine A + B and A x B. If an operation cannot be performed, explain why. 3 3 -2 B = 6 7]' -4 3.
Determine A + B and A x B. If an operation cannot be performed, explain why. -2 01 B = -6 3. 4. -9-
Determine A x B. -2 5 A = [3 2], B =
Determine A x B. 4 A = [2 -5 0], B = 6. -2
Determine A x B. B = A = 4 -2 -3 3 3. 4.
Determine A x B. 3 B =| 4 4 1
Determine A x B. -2] -2] B = -3
Determine A x B. Г4 21 3] 3 A = [3 :- 5 6, B = 3.
Determine the following.3B - 2C 2 3 -2 3 -2 and C = A = 4 5] I|
Determine the following.2B + 3C 2 3 -2 3 -2 and C = A = 4 5] I|
Determine the following.-3B 2 3 -2 3 -2 and C = A = 4 5] I|
Determine the following.2A 2 3 -2 3 -2 and C = A = 4 5] I|
Determine A - B. 3 3 -1 4 2 A =| 7 B = -2 -4 9 -5 0 -2 -5 -1
Determine A - B. -8 -6 -5 1 -5 -10 -11 B = -5 -7 -7 1
Determine A - B. 3 -3 10 12 B = -3 -9
Determine A - B. 6. -2 A B = 4 4-
Determine A + B. 3 3 -1 4 -6 1 -2 B = A -1 3 5 3 8 3. 3. 2. 2. 3.
Determine A + B. 5 2 -3 3 -4 B = -4 0 -1 4 -1 3.
Determine A + B. 4 7. B = -3 -3 0]
Determine A + B. -1 B = [2 -5 2. -8.

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