Contemporary Abstract Algebra
9th Edition
ISBN: 9781305657960
Author: Joseph Gallian
Publisher: Cengage Learning
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Chapter 1, Problem 22E
If F is a reflection in the dihedral group
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Chapter 1 Solutions
Contemporary Abstract Algebra
Ch. 1 - Prob. 1ECh. 1 - Prob. 2ECh. 1 - In D4 , find all elements X such that a. X3=V ; b....Ch. 1 - Prob. 4ECh. 1 - For n3 , describe the elements of Dn . (Hint: You...Ch. 1 - In Dn , explain geometrically why a reflection...Ch. 1 - Prob. 7ECh. 1 - Prob. 8ECh. 1 - Associate the number 1 with a rotation and the...Ch. 1 - If r1,r2,andr3 represent rotations from Dn and...
Ch. 1 - Suppose that a, b, and c are elements of a...Ch. 1 - Prob. 12ECh. 1 - Find elements A, B, and C in D4 such that AB=BC...Ch. 1 - Explain what the following diagram proves about...Ch. 1 - Prob. 15ECh. 1 - Describe the symmetries of a parallelogram that is...Ch. 1 - Describe the symmetries of a noncircular ellipse....Ch. 1 - Prob. 18ECh. 1 - Prob. 19ECh. 1 - Determine the symmetry group of the outer shell of...Ch. 1 - Let X,Y,R90 be elements of D4 with YR90andX2Y=R90...Ch. 1 - If F is a reflection in the dihedral group Dn find...Ch. 1 - What symmetry property do the words “mow,” “sis,”...Ch. 1 - For each design below, determine the symmetry...Ch. 1 - What group theoretic property do uppercase letters...
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- Here is an augmented matrix for a system of equations (three equations and three variables). Let the variables used be x, y, and z: 1 2 4 6 0 1 -1 3 0 0 1 4 Note: that this matrix is already in row echelon form. Your goal is to use this row echelon form to revert back to the equations that this represents, and then to ultimately solve the system of equations by finding x, y and z. Input your answer as a coordinate point: (x,y,z) with no spaces.arrow_forward1 3 -4 In the following matrix perform the operation 2R1 + R2 → R2. -2 -1 6 After you have completed this, what numeric value is in the a22 position?arrow_forward5 -2 0 1 6 12 Let A = 6 7 -1 and B = 1/2 3 -14 -2 0 4 4 4 0 Compute -3A+2B and call the resulting matrix R. If rij represent the individual entries in the matrix R, what numeric value is in 131? Input your answer as a numeric value only.arrow_forward
- 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 --> R2arrow_forwardThe 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.arrow_forwardLet 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.arrow_forward
- If -1 "[a446]-[254] 4b = -1 , find the values of a and b. ○ There is no solution for a and b. ○ There are infinite solutions for a and b. O a=3, b=3 O a=1, b=2 O a=2, b=1 O a=2, b=2arrow_forwardA student puts a 3x3 system of linear equations is into an augmented matrix. The student then correctly puts the augmented matrix into row echelon form (REF), which yields the following resultant matrix: -2 3 -0.5 10 0 0 0 -2 0 1 -4 Which of the following conclusions is mathematically supported by the work shown about system of linear equations? The 3x3 system of linear equations has no solution. ○ The 3x3 system of linear equations has infinite solutions. The 3x3 system of linear equations has one unique solution.arrow_forwardSolve the following system of equations using matrices: -2x + 4y = 8 and 4x - 3y = 9 Note: This is the same system of equations referenced in Question 14. If a single solution exists, express your solution as an (x,y) coordinate point with no spaces. If there are infinite solutions write inf and if there are no solutions write ns in the box.arrow_forward
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