EBK ALGEBRA AND TRIGONOMETRY
6th Edition
ISBN: 9780134383385
Author: Penna
Publisher: VST
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Chapter J.5, Problem 5E
To determine
To compute: 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 ALGEBRA AND TRIGONOMETRY
Ch. J.1 - In Exercises 1-6, consider the numbers
6, −2.45,...Ch. J.1 - In Exercises 1–6, consider the numbers
6, −2.45,...Ch. J.1 - In Exercises 1–6, consider the numbers
6, −2.45,...Ch. J.1 - In exercises 1–6, consider the numbers
6, −2.45,...Ch. J.1 - Prob. 5ECh. J.1 - In Exercises 1–6, consider the numbers
6, −2.45,...Ch. J.2 - Name the property illustrated by the sentence.
1....Ch. J.2 - Prob. 2ECh. J.2 - Prob. 3ECh. 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 <...Ch. J.3 - Prob. 2ECh. J.3 - Prob. 3ECh. 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 - Prob. 2ECh. 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 - Prob. 12ECh. 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 - Prob. 3ECh. J.6 - Prob. 4ECh. J.6 - Prob. 5ECh. J.6 - Prob. 6ECh. J.6 - Prob. 7ECh. J.6 - Prob. 8ECh. J.6 - Prob. 9ECh. J.6 - Prob. 10ECh. J.7 - Prob. 1ECh. 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 - Prob. 1ECh. J.8 - Prob. 2ECh. J.8 - Prob. 3ECh. J.8 - Prob. 4ECh. J.8 - Prob. 5ECh. J.8 - Prob. 6ECh. J.8 - Prob. 7ECh. J.8 - Prob. 8ECh. J.9 - Calculate.
1. 3 + 18 ÷ 6 − 3
Ch. 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 ∙ 256
Ch. J.9 - Calculate.
5. 26 ∙2−3 ÷ 210 ÷ 2−8
Ch. J.9 - Prob. 6ECh. J.9 - Prob. 7ECh. J.9 - Prob. 8ECh. J.10 - Determine the degree of the polynomial.
1. 5 − x6
Ch. 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 - Prob. 1ECh. J.11 - Prob. 2ECh. 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 - Prob. 1ECh. J.13 - Prob. 2ECh. J.13 - Prob. 3ECh. J.13 - Prob. 4ECh. J.13 - Prob. 5ECh. J.13 - Prob. 6ECh. J.14 - Prob. 1ECh. J.14 - Prob. 2ECh. J.14 - Prob. 3ECh. J.14 - Prob. 4ECh. J.14 - Prob. 5ECh. J.14 - Prob. 6ECh. J.14 - Factor the trinomial.
7. 2n2 − 20n − 48
Ch. J.14 - Prob. 8ECh. J.14 - Prob. 9ECh. J.14 - Prob. 10ECh. J.14 - Prob. 11ECh. J.14 - Prob. 12ECh. J.15 - Prob. 1ECh. J.15 - Prob. 2ECh. J.15 - Prob. 3ECh. J.16 - Factor the difference of squares.
1. z2 − 81
Ch. J.16 - Prob. 2ECh. J.16 - Prob. 3ECh. J.16 - Prob. 4ECh. J.16 - Prob. 5ECh. J.16 - Prob. 6ECh. J.16 - Prob. 7ECh. J.16 - Factor the sum or the difference of cubes.
8. m3 −...Ch. J.16 - Factor the sum or the difference of cubes.
9. 3a5...Ch. J.16 - Factor the sum or the difference of cubes.
10. t6...Ch. J.17 - Prob. 1ECh. J.17 - Prob. 2ECh. J.17 - Prob. 3ECh. J.17 - Prob. 4ECh. J.17 - Prob. 5ECh. J.17 - Prob. 6ECh. J.17 - Prob. 7ECh. J.17 - Prob. 8ECh. 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 - Find the domain of the rational expression.
1.
Ch. J.21 - Prob. 2ECh. J.21 - Prob. 3ECh. J.21 - Prob. 4ECh. J.21 - Simplify.
5.
Ch. J.21 - Simplify.
6.
Ch. J.22 - Multiply or divide and, if possible, simplify.
1....Ch. J.22 - Prob. 2ECh. J.22 - Prob. 3ECh. J.22 - Prob. 4ECh. J.22 - Multiply or divide and, if possible, simplify.
5....Ch. J.22 - Multiply or divide and, if possible, simplify.
6....Ch. J.23 - Add or subtract and, if possible, simplify.
1.
Ch. J.23 - Prob. 2ECh. J.23 - Prob. 3ECh. J.23 - Prob. 4ECh. J.23 - Add or subtract and, if possible, simplify.
5.
Ch. J.23 - Add or subtract and, if possible, simplify.
6.
Ch. J.24 - Simplify.
1.
Ch. J.24 - Prob. 2ECh. J.24 - Simplify.
3.
Ch. J.24 - Prob. 4ECh. J.24 - Simplify.
5.
Note: b − a = −1(a − b)
Ch. J.25 - Simplify. Assume that no radicands were formed by...Ch. 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 - Simplify. Assume that no radicands were formed by...Ch. J.25 - Simplify. Assume that no radicands were formed by...Ch. J.25 - Prob. 10ECh. J.25 - Prob. 11ECh. J.25 - Prob. 12ECh. J.25 - Simplify. Assume that no radicands were formed by...Ch. J.25 - Prob. 14ECh. J.25 - Prob. 15ECh. J.25 - Prob. 16ECh. J.25 - Simplify. Assume that no radicands were formed by...Ch. J.25 - Simplify. Assume that no radicands were formed by...Ch. J.25 - Prob. 19ECh. J.25 - Prob. 20ECh. J.26 - Rationalize the denominator.
1.
Ch. J.26 - Rationalize the denominator.
2.
Ch. J.26 - Prob. 3ECh. J.26 - Rationalize the denominator.
4.
Ch. J.26 - Prob. 5ECh. J.26 - Prob. 6ECh. J.26 - Prob. 7ECh. J.26 - Rationalize the denominator.
8.
Ch. J.27 - Convert to radical notation and, if possible,...Ch. J.27 - Prob. 2ECh. J.27 - Convert to radical notation and, if possible,...Ch. J.27 - Prob. 4ECh. J.27 - Convert to radical notation and, if possible,...Ch. J.27 - Prob. 6ECh. J.27 - Prob. 7ECh. J.27 - Prob. 8ECh. J.27 - Prob. 9ECh. J.27 - Prob. 10ECh. J.27 - Simplify and then, if appropriate, write radical...Ch. J.28 - Prob. 1ECh. J.28 - Prob. 2ECh. J.28 - Prob. 3ECh. J.28 - Prob. 4ECh. J.28 - Prob. 5E
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