The multiplicative inverse of 1+ 3x in Z,[x] is: None 1/(3x+1) O 4x+1 О бх+1

Q: Find the inverse of R= 0, if it exists. 1 3 1 1 3 1 R- does not exist.

A: Matrix of inverse is exist iff determinant of a matrix is non zero.

Q: In the ring Z[x]/ 1- The inverse of x is: a) x+1 b) x2 +1 c) x d) x? 2- The value that replacesx is…

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Q: Verify that for all x, the change-of-base formula holds: bx = ax Ioga b for a, b > 0 such that a…

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Q: Suppose B is the inverse of A2. Prove that AB is the inverse of A.

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Q: x - x3 + x² – x + 1 is reducible over Q True False

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Q: Use Gauss-Jordan method to calculate the inverse of A A-l = |1 0 -1 A =| 0 1 1 1 1 1

A: By Gauss Jordan Elimination method the inverse of matrix is given as follows :

Q: In the ring Z:[x] 1- The inverse of xis: a) x+1 b) x+1 c) x d) x 2- The value thatreplacesx is a)…

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Q: The multiplicative inverse of x* + x+1 in Z,[x]/ is: O x^3 X+1 X^4 None

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: The multiplicative inverse of x* + x +1 in Z,[x]/ is: O x^3 O x^4 x+1 None

A: The given expression is x4+x+1. We have to find the inverse of the given expression in…

Q: 2) Show that additive inverse of any z = (x, y) E Cis unique and it equals-z = (-x, -y). Show that…

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Q: In the ring Z;[x]': 1- The inverse of x is:

A: Answer :

Q: Exercise 5.4.18. Give a similar proof that 1 is the multiplicative identity for Zn when n > 1. What…

A: To show 1 is the multiplicative identity of  ℤn for n>1 and 0 is the multiplicative identity of…

Q: Exercise 8.5. (a) Is Z₁ Z6 isomorphic to Z24? (b) Is Z3 Z7 isomorphic to Z21? (c) Is Z10 Z20…

A: 8.5 (a) Is ℤ4⊕ℤ6 is isomorphic to ℤ24? (b) Is ℤ3⊕ℤ7 is isomorphic to ℤ21? (c) Is ℤ10⊕ℤ20 is…

Q: Which of the following is homogenous of smallest degree? (A) In x - In y B x+y x-y C √x-y x² + y4 X…

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Q: In the ring Z[x] 1- The inverse of x is: a) x+1 b) x+1 c) x d) x 2- The value that replacesx is a)…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: The multiplicative inverse of x+ x +1 in Z,[x]/ is: O None O x^4 x+1 x^3

A: I will use the definition of multiplicative inverse.

Q: The multiplicative inverse of x? + x in Z2[x]/ is:

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Q: Let n be a positive integer. The coefficient of x°y° in the expansion of (1+ xy+ y²)' equals

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Q: Use the inverse form of the first translation theorem to determine the power of e. 2! %3D (S-5)° -5t…

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Q: In the ring Z[x] 1- The inverse of x² is a) x+1 b) x2+1 c) x d) x2 2- The value that replaces x is…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: In Z[i], show that 3 is irreducible but 2 and 5 are not

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Q: Show that is isomorphic to Z2.

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Q: Compute only one the inverse z-transform of 02 a) X(z) = 5)X(z) = Q3 ROGIZ| >3- ROC Z > 3 %3D %3D…

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Q: Find the set of all values of a for which f(x) = x° +(a + 2)x² + 3ax + 5 is invertible.

A: We know that, for function to be invertible the discriminant of its first order derivative should be…

Q: Show that – a is the inverse of a for the addition operation ‘+’ on R and1/a is the inverse of a ≠ 0…

A: An element ‘a’ in R is invertible if there is an element b in R.Such that,

Q: The multiplicative inverse of x+ x+1 in Z, [x]/ is: None X+1 X^4 X^3

A:

Q: 2) Show that additive inverse of any z = (x, y) E C is unique and it equals-z = (-x, -y). Show that…

A: Let additive inverse of Z = (x14) E C is (a,b) Then, Z + (a,b) = (0,0) As (0,0) is identity in…

Q: In the ring Z:[x]/ 1- The inverse of x is: a) x+1 b) x+1 c) x d) x 2- The value that replacesx is a)…

A: " Since you have posted a question with multi subparts. We will solve first three parts for you. To…

Q: 9. The inverse of an element a of Z under the operation * defined as a*b = a + b - 1 is_ A. a -2…

A: Given ;a*b=a+b-1

Q: Which of the following is homogenous of smallest degree? A In x - In y x-y B /x-y x4+y* x+y

A: Let's find.

Q: 39 In Z,[x], let I = (r + x + 2). Find the multiplicative inverse of 2x + 3+I inZ.[x\/I.,

A: Given:         In Z5x , I =x2+x+2   To find multiplicative inverse of 2x+3+I is   By dividing…

Q: The multiplicative inverse of x*+x+1 in Z,[x]/ is: X+1 X^4 3 None

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Q: 4 Let [a] e Z. Use Theorem 212 to prove if a and n are relativelyprime then [a] has a multiplicative…

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Q: Let H(x):=k for x=, (keN) and H(x):=0 elsewhere on [0,1] Show that H(x) 4ER[0,1].

A: In this question, we use the definition of Riemann integral to check the function H(x) is Riemann…

Q: In the ring Z[x]/ 1- The inverse of x² is a) x+1 b) x² +1 с) х d) x2 2- The value that replaces x is…

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Q: Prove: [a] is an element of Zn has a multiplicative inverse if and only if gcd(a,n)=

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Q: The identity element of binary operation defined on ℝ by x * y= xy  is

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Q: Let a ∈ R[[x]] with a0 not equal to 0. Prove that a has a multiplicative inverse in R[[x]]. You may…

A: We have given that , a∈ℝx a = a0 + a1x + a2x2 + ......  where each ai ∈ ℝ. Since , 1 ∈ ℝx  is an…

Q: Let z (х, у). Show that z- 2' 2 X + y -

A: We have to find the multiplicative inverse of z.

Q: In the ring Z[x]/: 1- The inverse of x is:

A: The given ring is ℤ2x/x3+1. The objective is to find the inverse of x and to find Uℤ⊕ℤ.

Q: Find the fnckion below the inverse of %3D

A: given function is                                                      y=x2+4 we have to find…

Q: In the ring Z:[x] 1- The inverse of xis: a) x+1 あ)+1 c) x d) x 2- The value that replacesx* is a)…

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Q: The inverse with respect to the binary operation on R defined by x • y=-

A: Given; x ° y= (x+y)/6

Q: that N(ry) = N(x)N(y) for all x and y in 22). 2. If x is invertible in Z[1], show that N(x) must…

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Q: Prove that the product xy of two real numbers x and y is nonnegative if if and only if the absolute…

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Q: 1 1 -1] C= 2 0 2 , rank(C)=2 101

A: Det(C) = 1(0-0) - 1(2-2) + (-1)(0)            =0

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.