Whether the polynomial 2 x 4 + 4 x 3 + 4 x + 3 is an element of I or not, where I be the principal ideal ( x 2 + 1 ) = { ( x 2 + 1 ) f ( x ) | f ( x ) ∈ Z 5 [ x ] } .

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Answer 1

Question

Chapter 8.2, Problem 20E

a)

To determine

Whether the polynomial 2x4+4x3+4x+3 is an element of I or not, where I be the principal ideal (x2+1)={(x2+1)f(x)|f(x)∈Z5[x]}.

b)

To determine

Whether the polynomial 3x5+x4+2x3+3x2+4x+1 is an element of I or not, where I be the principal ideal (x2+1)={(x2+1)f(x)|f(x)∈Z5[x]}.

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1 -2 4 10 My goal is to put the matrix 5 -1 1 0 into row echelon form using Gaussian elimination. 3 -2 6 9 My next step is to manipulate this matrix using elementary row operations to get a 0 in the a21 position. Which of the following operations would be the appropriate elementary row operation to use to get a 0 in the a21 position? O (1/5)*R2 --> R2 ○ 2R1 + R2 --> R2 ○ 5R1+ R2 --> R2 O-5R1 + R2 --> R2

The 2x2 linear system of equations -2x+4y = 8 and 4x-3y = 9 was put into the following -2 4 8 augmented matrix: 4 -3 9 This augmented matrix is then converted to row echelon form. Which of the following matrices is the appropriate row echelon form for the given augmented matrix? 0 Option 1: 1 11 -2 Option 2: 4 -3 9 Option 3: 10 ܂ -2 -4 5 25 1 -2 -4 Option 4: 0 1 5 1 -2 Option 5: 0 0 20 -4 5 ○ Option 1 is the appropriate row echelon form. ○ Option 2 is the appropriate row echelon form. ○ Option 3 is the appropriate row echelon form. ○ Option 4 is the appropriate row echelon form. ○ Option 5 is the appropriate row echelon form.

Let matrix A have order (dimension) 2x4 and let matrix B have order (dimension) 4x4. What results when you compute A+B? The resulting matrix will have dimensions of 2x4. ○ The resulting matrix will be a single number (scalar). The resulting matrix will have dimensions of 4x4. A+B is undefined since matrix A and B do not have the same dimensions.

Answer 2

Question

Chapter 8.2, Problem 20E

a)

To determine

Whether the polynomial 2x4+4x3+4x+3 is an element of I or not, where I be the principal ideal (x2+1)={(x2+1)f(x)|f(x)∈Z5[x]}.

b)

To determine

Whether the polynomial 3x5+x4+2x3+3x2+4x+1 is an element of I or not, where I be the principal ideal (x2+1)={(x2+1)f(x)|f(x)∈Z5[x]}.

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Answer 3

Question

Chapter 8.2, Problem 20E

a)

To determine

Whether the polynomial 2x4+4x3+4x+3 is an element of I or not, where I be the principal ideal (x2+1)={(x2+1)f(x)|f(x)∈Z5[x]}.

b)

To determine

Whether the polynomial 3x5+x4+2x3+3x2+4x+1 is an element of I or not, where I be the principal ideal (x2+1)={(x2+1)f(x)|f(x)∈Z5[x]}.

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Answer 4

Question

Chapter 8.2, Problem 20E

a)

To determine

Whether the polynomial 2x4+4x3+4x+3 is an element of I or not, where I be the principal ideal (x2+1)={(x2+1)f(x)|f(x)∈Z5[x]}.

b)

To determine

Whether the polynomial 3x5+x4+2x3+3x2+4x+1 is an element of I or not, where I be the principal ideal (x2+1)={(x2+1)f(x)|f(x)∈Z5[x]}.

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Answer 5

Chapter 8.2, Problem 20E

a)

To determine

Whether the polynomial 2x4+4x3+4x+3 is an element of I or not, where I be the principal ideal (x2+1)={(x2+1)f(x)|f(x)∈Z5[x]}.

b)

To determine

Whether the polynomial 3x5+x4+2x3+3x2+4x+1 is an element of I or not, where I be the principal ideal (x2+1)={(x2+1)f(x)|f(x)∈Z5[x]}.

Answer 6

Chapter 8.2, Problem 20E

a)

To determine

Whether the polynomial 2x4+4x3+4x+3 is an element of I or not, where I be the principal ideal (x2+1)={(x2+1)f(x)|f(x)∈Z5[x]}.

Answer 7

Chapter 8.2, Problem 20E

a)

To determine

Whether the polynomial 2x4+4x3+4x+3 is an element of I or not, where I be the principal ideal (x2+1)={(x2+1)f(x)|f(x)∈Z5[x]}.

Answer 8

b)

To determine

Whether the polynomial 3x5+x4+2x3+3x2+4x+1 is an element of I or not, where I be the principal ideal (x2+1)={(x2+1)f(x)|f(x)∈Z5[x]}.

Answer 9

b)

To determine

Whether the polynomial 3x5+x4+2x3+3x2+4x+1 is an element of I or not, where I be the principal ideal (x2+1)={(x2+1)f(x)|f(x)∈Z5[x]}.

Answer 10

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Answer 11

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Answer 12

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Answer 13

Ch. 8.1 - True or False Label each of the following...Ch. 8.1 - Prob. 2TFE Ch. 8.1 - Prob. 3TFE Ch. 8.1 - Prob. 4TFE Ch. 8.1 - Prob. 5TFE Ch. 8.1 - Prob. 6TFE Ch. 8.1 - Prob. 7TFE Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E

Whether the polynomial 2 x 4 + 4 x 3 + 4 x + 3 is an element of I or not, where I be the principal ideal ( x 2 + 1 ) = { ( x 2 + 1 ) f ( x ) | f ( x ) ∈ Z 5 [ x ] } .

Solution Summary: The author explains how to determine if the polynomial 2x4+4x+3 is an element of I. The principal ideal (a)=

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Whether the polynomial 2x4+4x3+4x+3 is an element of I or not, where I be the principal ideal (x2+1)={(x2+1)f(x)|f(x)∈Z5[x]}.

Whether the polynomial 3x5+x4+2x3+3x2+4x+1 is an element of I or not, where I be the principal ideal (x2+1)={(x2+1)f(x)|f(x)∈Z5[x]}.

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