EBK COLLEGE ALGEBRA
6th Edition
ISBN: 8220102019645
Author: Penna
Publisher: PEARSON
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Question
Chapter J.7, Problem 6E
To determine
To simplify: The expression
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Q.1) Classify the following statements as a true or false statements:
a. If M is a module, then every proper submodule of M is contained in a maximal
submodule of M.
b. The sum of a finite family of small submodules of a module M is small in M.
c. Zz is directly indecomposable.
d. An epimorphism a: M→ N is called solit iff Ker(a) is a direct summand in M.
e. The Z-module has two composition series.
Z
6Z
f. Zz does not have a composition series.
g. Any finitely generated module is a free module.
h. If O→A MW→ 0 is short exact sequence then f is epimorphism.
i. If f is a homomorphism then f-1 is also a homomorphism.
Maximal C≤A if and only if is simple.
Sup
Q.4) Give an example and explain your claim in each case:
Monomorphism not split.
b) A finite free module.
c) Semisimple module.
d) A small submodule A of a module N and a homomorphism op: MN, but
(A) is not small in M.
I need diagram with solutions
Chapter J Solutions
EBK COLLEGE ALGEBRA
Ch. J.1 - In Exercises 1-6, consider the numbers 23, 6, 3,...Ch. J.1 - In Exercises 16, consider the numbers 23, 6, 3,...Ch. J.1 - In Exercises 16, consider the numbers 23, 6, 3,...Ch. J.1 - In exercises 16, consider the numbers 23, 6, 3,...Ch. J.1 - In Exercises 16, consider the numbers 23, 6, 3,...Ch. J.1 - In Exercises 16, consider the numbers 23, 6, 3,...Ch. J.2 - Name the property illustrated by the sentence. 1....Ch. J.2 - Name the property illustrated by the sentence. 2....Ch. J.2 - Name the property illustrated by the sentence. 3....Ch. J.2 - Prob. 4E
Ch. J.2 - Prob. 5ECh. J.2 - Prob. 6ECh. J.2 - Prob. 7ECh. J.2 - Prob. 8ECh. J.2 - Prob. 9ECh. J.2 - Prob. 10ECh. J.3 - Classify the inequality as true or false. 1. 9 9Ch. J.3 - Prob. 2ECh. J.3 - Classify the inequality as true or false. 3. 265Ch. J.3 - Prob. 4ECh. J.3 - Prob. 5ECh. J.3 - Prob. 6ECh. J.4 - Simplify. 1. |98|Ch. J.4 - Prob. 2ECh. J.4 - Prob. 3ECh. J.4 - Prob. 4ECh. J.4 - Prob. 5ECh. J.4 - Prob. 6ECh. J.4 - Prob. 7ECh. J.4 - Prob. 8ECh. J.5 - Compute and simplify. 1. 8 (11)Ch. J.5 - Compute and simplify. 2. 310(13)Ch. J.5 - Prob. 3ECh. J.5 - Prob. 4ECh. J.5 - Prob. 5ECh. J.5 - Prob. 6ECh. J.5 - Prob. 7ECh. J.5 - Prob. 8ECh. J.5 - Prob. 9ECh. J.5 - Prob. 10ECh. J.5 - Prob. 11ECh. J.5 - Compute and simplify. 12. 1223Ch. J.5 - Prob. 13ECh. J.5 - Prob. 14ECh. J.5 - Prob. 15ECh. J.6 - Write interval notation. 1. {x| 5 x 5}Ch. J.6 - Prob. 2ECh. J.6 - Write interval notation. 3. {x | x 2}Ch. J.6 - Write interval notation. 4. {x | x 3.8}Ch. J.6 - Prob. 5ECh. J.6 - Prob. 6ECh. J.6 - Prob. 7ECh. J.6 - Prob. 8ECh. J.6 - Prob. 9ECh. J.6 - Write interval notation for the graph. 10.Ch. J.7 - Simplify. 1. 36Ch. J.7 - Prob. 2ECh. J.7 - Prob. 3ECh. J.7 - Prob. 4ECh. J.7 - Prob. 5ECh. J.7 - Prob. 6ECh. J.7 - Prob. 7ECh. J.7 - Prob. 8ECh. J.7 - Prob. 9ECh. J.7 - Prob. 10ECh. J.8 - Convert to scientific notation. 1. 18,500,000Ch. J.8 - Prob. 2ECh. J.8 - Prob. 3ECh. J.8 - Prob. 4ECh. J.8 - Convert to decimal notation. 5.4.3 108Ch. J.8 - Prob. 6ECh. J.8 - Convert to decimal notation. 7.6.203 1011Ch. J.8 - Prob. 8ECh. J.9 - Calculate. 1. 3 + 18 6 3Ch. J.9 - Calculate. 2. 5 3 + 8 32 + 4(6 2)Ch. J.9 - Calculate. 3. 5(3 8 32 + 4 6 2)Ch. J.9 - Calculate. 4. 16 4 4 2 256Ch. J.9 - Calculate. 5. 26 23 210 28Ch. J.9 - Calculate. 6. 4(86)243+2831+190Ch. J.9 - Calculate. 7. 64 [(4) (2)]Ch. J.9 - Prob. 8ECh. J.10 - Determine the degree of the polynomial. 1. 5 x6Ch. J.10 - Prob. 2ECh. J.10 - Prob. 3ECh. J.10 - Prob. 4ECh. J.10 - Prob. 5ECh. J.10 - Prob. 6ECh. J.10 - Prob. 7ECh. J.10 - Prob. 8ECh. J.11 - Add or subtract. 1. (8y 1) (3 y)Ch. J.11 - Add or subtract. 2. (3x2 2x x3 + 2) (5x2 8x ...Ch. J.11 - Prob. 3ECh. J.11 - Prob. 4ECh. J.11 - Prob. 5ECh. J.12 - Prob. 1ECh. J.12 - Prob. 2ECh. J.12 - Prob. 3ECh. J.12 - Prob. 4ECh. J.12 - Prob. 5ECh. J.12 - Prob. 6ECh. J.13 - Multiply. 1. (x + 3)2Ch. J.13 - Multiply. 2. (5x 3)2Ch. J.13 - Multiply. 3. (2x + 3y)2Ch. J.13 - Prob. 4ECh. J.13 - Multiply. 5. (n + 6) (n 6)Ch. J.13 - Prob. 6ECh. J.14 - Factor out the largest common factor. 1. 3x + 18Ch. J.14 - Prob. 2ECh. J.14 - Prob. 3ECh. J.14 - Prob. 4ECh. J.14 - Prob. 5ECh. J.14 - Prob. 6ECh. J.14 - Prob. 7ECh. J.14 - Prob. 8ECh. J.14 - Prob. 9ECh. J.14 - Prob. 10ECh. J.14 - Prob. 11ECh. J.14 - Prob. 12ECh. J.15 - Factor. 1. 8x2 6x 9Ch. J.15 - Factor. 2. 10t2 + 4t 6Ch. J.15 - Factor. 3. 18a2 51a + 15Ch. J.16 - Factor the difference of squares. 1. z2 81Ch. J.16 - Factor the difference of squares. 2. 16x2 9Ch. J.16 - Factor the difference of squares. 3. 7pq4 7py4Ch. J.16 - Factor the square of a binomial. 4. x2 + 12x + 36Ch. J.16 - Prob. 5ECh. J.16 - Factor the square of a binomial. 6. a3 + 24a2 +...Ch. J.16 - Factor the sum or the difference of cubes. 7. x3 +...Ch. J.16 - Factor the sum or the difference of cubes. 8. m3 ...Ch. J.16 - Prob. 9ECh. J.16 - Prob. 10ECh. J.17 - Prob. 1ECh. J.17 - Prob. 2ECh. J.17 - Prob. 3ECh. J.17 - Prob. 4ECh. J.17 - Solve. 5. 7y 1 = 23 5yCh. J.17 - Prob. 6ECh. J.17 - Prob. 7ECh. J.17 - Solve. 8. 5y 4 (2y 10) = 25Ch. J.18 - Prob. 1ECh. J.18 - Prob. 2ECh. J.18 - Prob. 3ECh. J.18 - Prob. 4ECh. J.18 - Prob. 5ECh. J.18 - Prob. 6ECh. J.19 - Prob. 1ECh. J.19 - Prob. 2ECh. J.19 - Prob. 3ECh. J.19 - Prob. 4ECh. J.19 - Prob. 5ECh. J.19 - Prob. 6ECh. J.19 - Prob. 7ECh. J.19 - Prob. 8ECh. J.20 - Prob. 1ECh. J.20 - Prob. 2ECh. J.20 - Prob. 3ECh. J.20 - Prob. 4ECh. J.20 - Prob. 5ECh. J.20 - Prob. 6ECh. J.21 - Prob. 1ECh. J.21 - Prob. 2ECh. J.21 - Prob. 3ECh. J.21 - Prob. 4ECh. J.21 - Prob. 5ECh. J.21 - Prob. 6ECh. J.22 - Prob. 1ECh. J.22 - Prob. 2ECh. J.22 - Prob. 3ECh. J.22 - Prob. 4ECh. J.22 - Prob. 5ECh. J.22 - Prob. 6ECh. J.23 - Prob. 1ECh. J.23 - Prob. 2ECh. J.23 - Prob. 3ECh. J.23 - Prob. 4ECh. J.23 - Prob. 5ECh. J.23 - Prob. 6ECh. J.24 - Simplify. 1. xyyx1y+1xCh. J.24 - Prob. 2ECh. J.24 - Prob. 3ECh. J.24 - Prob. 4ECh. J.24 - Simplify. 5. abba1a1b Note: b a = 1(a b)Ch. J.25 - Prob. 1ECh. J.25 - Prob. 2ECh. J.25 - Prob. 3ECh. J.25 - Prob. 4ECh. J.25 - Prob. 5ECh. J.25 - Prob. 6ECh. J.25 - Prob. 7ECh. J.25 - Prob. 8ECh. J.25 - Prob. 9ECh. J.25 - Prob. 10ECh. J.25 - Prob. 11ECh. J.25 - Prob. 12ECh. J.25 - Prob. 13ECh. J.25 - Prob. 14ECh. J.25 - Prob. 15ECh. J.25 - Prob. 16ECh. J.25 - Prob. 17ECh. J.25 - Prob. 18ECh. J.25 - Prob. 19ECh. J.25 - Prob. 20ECh. J.26 - Prob. 1ECh. J.26 - Prob. 2ECh. J.26 - Prob. 3ECh. J.26 - Prob. 4ECh. J.26 - Prob. 5ECh. J.26 - Prob. 6ECh. J.26 - Prob. 7ECh. J.26 - Prob. 8ECh. J.27 - Prob. 1ECh. J.27 - Prob. 2ECh. J.27 - Prob. 3ECh. J.27 - Prob. 4ECh. J.27 - Prob. 5ECh. J.27 - Prob. 6ECh. J.27 - Prob. 7ECh. J.27 - Convert to exponential notation. 8. x5Ch. J.27 - Prob. 9ECh. J.27 - Prob. 10ECh. J.27 - Prob. 11ECh. J.28 - Find the length of the third side of each right...Ch. J.28 - Find the length of the third side of each right...Ch. J.28 - Find the length of the third side of each right...Ch. J.28 - Find the length of the third side of each right...Ch. J.28 - Find the length of the third side of each right...
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- T. Determine the least common denominator and the domain for the 2x-3 10 problem: + x²+6x+8 x²+x-12 3 2x 2. Add: + Simplify and 5x+10 x²-2x-8 state the domain. 7 3. Add/Subtract: x+2 1 + x+6 2x+2 4 Simplify and state the domain. x+1 4 4. Subtract: - Simplify 3x-3 x²-3x+2 and state the domain. 1 15 3x-5 5. Add/Subtract: + 2 2x-14 x²-7x Simplify and state the domain.arrow_forwardQ.1) Classify the following statements as a true or false statements: Q a. A simple ring R is simple as a right R-module. b. Every ideal of ZZ is small ideal. very den to is lovaginz c. A nontrivial direct summand of a module cannot be large or small submodule. d. The sum of a finite family of small submodules of a module M is small in M. e. The direct product of a finite family of projective modules is projective f. The sum of a finite family of large submodules of a module M is large in M. g. Zz contains no minimal submodules. h. Qz has no minimal and no maximal submodules. i. Every divisible Z-module is injective. j. Every projective module is a free module. a homomorp cements Q.4) Give an example and explain your claim in each case: a) A module M which has a largest proper submodule, is directly indecomposable. b) A free subset of a module. c) A finite free module. d) A module contains no a direct summand. e) A short split exact sequence of modules.arrow_forwardListen ANALYZING RELATIONSHIPS Describe the x-values for which (a) f is increasing or decreasing, (b) f(x) > 0 and (c) f(x) <0. y Af -2 1 2 4x a. The function is increasing when and decreasing whenarrow_forwardBy forming the augmented matrix corresponding to this system of equations and usingGaussian elimination, find the values of t and u that imply the system:(i) is inconsistent.(ii) has infinitely many solutions.(iii) has a unique solutiona=2 b=1arrow_forwardif a=2 and b=1 1) Calculate 49(B-1)2+7B−1AT+7ATB−1+(AT)2 2)Find a matrix C such that (B − 2C)-1=A 3) Find a non-diagonal matrix E ̸= B such that det(AB) = det(AE)arrow_forwardWrite the equation line shown on the graph in slope, intercept form.arrow_forward1.2.15. (!) Let W be a closed walk of length at least 1 that does not contain a cycle. Prove that some edge of W repeats immediately (once in each direction).arrow_forward1.2.18. (!) Let G be the graph whose vertex set is the set of k-tuples with elements in (0, 1), with x adjacent to y if x and y differ in exactly two positions. Determine the number of components of G.arrow_forward1.2.17. (!) Let G,, be the graph whose vertices are the permutations of (1,..., n}, with two permutations a₁, ..., a,, and b₁, ..., b, adjacent if they differ by interchanging a pair of adjacent entries (G3 shown below). Prove that G,, is connected. 132 123 213 312 321 231arrow_forward1.2.19. Let and s be natural numbers. Let G be the simple graph with vertex set Vo... V„−1 such that v; ↔ v; if and only if |ji| Є (r,s). Prove that S has exactly k components, where k is the greatest common divisor of {n, r,s}.arrow_forward1.2.20. (!) Let u be a cut-vertex of a simple graph G. Prove that G - v is connected. עarrow_forward1.2.12. (-) Convert the proof at 1.2.32 to an procedure for finding an Eulerian circuit in a connected even graph.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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