Intermediate Algebra (12th Edition)
12th Edition
ISBN: 9780321924711
Author: Marvin L. Bittinger
Publisher: PEARSON
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Chapter A, Problem 14ES
b Simplify.
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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 when
By 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=1
if 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)
Chapter A Solutions
Intermediate Algebra (12th Edition)
Ch. A - 1. Write a fraction expression equivalent to with...Ch. A - Write a fraction expression equivalent to 34 with...Ch. A - Multiply by 1 to find three different fraction...Ch. A - Simplify. 1845Ch. A - Simplify.
5.
Ch. A - Simplify. 7227Ch. A - Simplify. 3256Ch. A - Simplify. 2754Ch. A - Simplify. 4812Ch. A - Multiply and simplify. 652512
Ch. A - Multiply and simplify. 385372Ch. A - Add and simplify. 45+35Ch. A - Add and simplify.
13.
Ch. A - Add and simplify.
14.
Ch. A - Add and simplify.
15.
Ch. A - Subtract and simplify.
16.
Ch. A - Subtract and simplify. 51229Ch. A - Find each reciprocal. 411Ch. A - Find each reciprocal. 157Ch. A - Find each reciprocal. 5Ch. A - Find each reciprocal. 13Ch. A - 22. Divide by multiplying by 1:
Ch. A - Divide by multiplying by the reciprocal of the...Ch. A - Divide by multiplying by the reciprocal of the...Ch. A - Divide by multiplying by the reciprocal of the...Ch. A - Divide by multiplying by the reciprocal of the...Ch. A - Divide and simplify.
27.
Ch. A - Divide and simplify.
28.
Ch. A - a Write an equivalent expression for each of the...Ch. A - a Write an equivalent expression for each of the...Ch. A - a Write an equivalent expression for each of the...Ch. A - a Write an equivalent expression for each of the...Ch. A - Write an equivalent expression with the given...Ch. A - Write an equivalent expression with the given...Ch. A - b Simplify. 1827Ch. A - b Simplify.
8.
Ch. A - b Simplify. 5614Ch. A - b Simplify. 4827Ch. A - b Simplify. 642Ch. A - b Simplify. 13104Ch. A - b Simplify. 567Ch. A - b Simplify. 13211Ch. A - b Simplify. 1976Ch. A - b Simplify. 1751Ch. A - b Simplify. 10020Ch. A - b Simplify. 15025Ch. A - b Simplify.
19.
Ch. A - b Simplify. 625325Ch. A - b Simplify.
21.
Ch. A - b Simplify. 48001600Ch. A - b Simplify.
23.
Ch. A - b Simplify.
24.
Ch. A - c Compute and simplify.
25.
Ch. A - c Compute and simplify. 151685Ch. A - c Compute and simplify.
27.
Ch. A - c Compute and simplify. 10111110Ch. A - c Compute and simplify.
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Ch. A - c Compute and simplify. 45+815Ch. A - c Compute and simplify. 310+815Ch. A - c Compute and simplify. 98+712Ch. A - c Compute and simplify. 5434Ch. A - c Compute and simplify.
34.
Ch. A - c Compute and simplify.
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Ch. A - c Compute and simplify.
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Ch. A - c Compute and simplify.
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Ch. A - c Compute and simplify.
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Ch. A - c Compute and simplify. 89415Ch. A - c Compute and simplify.
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Ch. A - c Compute and simplify. 1312395Ch. A - c Compute and simplify.
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Ch. A - c Compute and simplify. 10015Ch. A - c Compute and simplify. 7816Ch. A - c Compute and simplify. 3410Ch. A - c Compute and simplify.
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Ch. A - c Compute and simplify.
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Ch. A - c Compute and simplify. 147502
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- Write 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_forward
- 1.2.17. (!) 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_forward
- 1.2.12. (-) Convert the proof at 1.2.32 to an procedure for finding an Eulerian circuit in a connected even graph.arrow_forward1.2.16. Let e be an edge appearing an odd number of times in a closed walk W. Prove that W contains the edges of a cycle through c.arrow_forward1.2.11. (−) Prove or disprove: If G is an Eulerian graph with edges e, f that share vertex, then G has an Eulerian circuit in which e, f appear consecutively. aarrow_forward
- By 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_forward1.2.6. (-) In the graph below (the paw), find all the maximal paths, maximal cliques, and maximal independent sets. Also find all the maximum paths, maximum cliques, and maximum independent sets.arrow_forward1.2.13. Alternative proofs that every u, v-walk contains a u, v-path (Lemma 1.2.5). a) (ordinary induction) Given that every walk of length 1-1 contains a path from its first vertex to its last, prove that every walk of length / also satisfies this. b) (extremality) Given a u, v-walk W, consider a shortest u, u-walk contained in W.arrow_forward
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