Pearson eText for Finite Mathematics & Its Applications -- Instant Access (Pearson+)
12th Edition
ISBN: 9780137442966
Author: Larry Goldstein, David Schneider
Publisher: PEARSON+
expand_more
expand_more
format_list_bulleted
Videos
Question
Chapter 1.2, Problem 70E
To determine
The equation of a line which is perpendicular to the line
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The cup on the 9th hole of a golf course is located dead center in the middle of a circular green which is 40 feet in radius. Your ball is located as in the picture below. The ball follows a straight line path and exits the green at the right-most edge. Assume the ball travels 8 ft/sec.
Introduce coordinates so that the cup is the origin of an xy-coordinate system and start by writing down the equations of the circle and the linear path of the ball. Provide numerical answers below with two decimal places of accuracy.
50 feet
green
ball
40 feet
9
cup
ball path
rough
(a) The x-coordinate of the position where the ball enters the green will be
(b) The ball will exit the green exactly
seconds after it is hit.
(c) Suppose that L is a line tangent to the boundary of the golf green and parallel to the path of the ball. Let Q be the point where the line is tangent to the circle. Notice that there are two possible positions for Q. Find the possible x-coordinates of Q:
smallest x-coordinate =…
Draw the unit circle and plot the point P=(8,2). Observe there are TWO lines tangent to the circle passing through the point P. Answer the questions below with 3 decimal places of accuracy.
P
L1
L
(a) The line L₁ is tangent to the unit circle at the point
(b) The tangent line L₁ has equation:
X +
(c) The line L₂ is tangent to the unit circle at the point (
(d) The tangent line 42 has equation:
y=
x +
).
Introduce yourself and describe a time when you used data in a personal or professional decision. This could be anything from analyzing sales data on the job to making an informed purchasing decision about a home or car.
Describe to Susan how to take a sample of the student population that would not represent the population well.
Describe to Susan how to take a sample of the student population that would represent the population well.
Finally, describe the relationship of a sample to a population and classify your two samples as random, systematic, cluster, stratified, or convenience.
Chapter 1 Solutions
Pearson eText for Finite Mathematics & Its Applications -- Instant Access (Pearson+)
Ch. 1.1 - Plot the point (500,200).Ch. 1.1 - 2. Is the point on the graph of the linear...Ch. 1.1 - In Exercises 1–8, plot the given point.
1.
Ch. 1.1 - In Exercises 18, plot the given point. (1,4)Ch. 1.1 - In Exercises 1–8, plot the given point.
3.
Ch. 1.1 - In Exercises 18, plot the given point. (2,0)Ch. 1.1 - In Exercises 18, plot the given point. (2,1)Ch. 1.1 - In Exercises 18, plot the given point. (1,52)Ch. 1.1 - In Exercises 1–8, plot the given point.
7.
Ch. 1.1 - In Exercises 1–8, plot the given point.
8.
Ch. 1.1 - What are the coordinates of the point Q in Fig. 7?Ch. 1.1 - What are the coordinates of the point P in Fig. 7?Ch. 1.1 - In Exercises 11–14, determine whether the point is...Ch. 1.1 - In Exercises 1114, determine whether the point is...Ch. 1.1 - In Exercises 11–14, determine whether the point is...Ch. 1.1 - In Exercises 1114, determine whether the point is...Ch. 1.1 - In Exercises 15–18, each linear equation is in the...Ch. 1.1 - In Exercises 1518, each linear equation is in the...Ch. 1.1 - In Exercises 1518, each linear equation is in the...Ch. 1.1 - In Exercises 1518, each linear equation is in the...Ch. 1.1 - In Exercises 19–22, write each linear equation in...Ch. 1.1 - In Exercises 1922, write each linear equation in...Ch. 1.1 - In Exercises 1922, write each linear equation in...Ch. 1.1 - In Exercises 19–22, write each linear equation in...Ch. 1.1 - In Exercises 2326, find the x-intercept and the...Ch. 1.1 - In Exercises 2326, find the x-intercept and the...Ch. 1.1 - In Exercises 2326, find the x-intercept and the...Ch. 1.1 - In Exercises 2326, find the x-intercept and the...Ch. 1.1 - In Exercises 2734, graph the given linear...Ch. 1.1 - In Exercises 2734, graph the given linear...Ch. 1.1 - In Exercises 27–34, graph the given linear...Ch. 1.1 - In Exercises 2734, graph the given linear...Ch. 1.1 - In Exercises 27–34, graph the given linear...Ch. 1.1 - In Exercises 2734, graph the given linear...Ch. 1.1 - In Exercises 27–34, graph the given linear...Ch. 1.1 - In Exercises 2734, graph the given linear...Ch. 1.1 - Which of the following equations describe the same...Ch. 1.1 - Which of the following equations describe the same...Ch. 1.1 - 37. Each of the lines in Fig. 8 is the graph of...Ch. 1.1 - 38. Which of the following equations is graphed in...Ch. 1.1 - 39. Heating Water The temperature of water in a...Ch. 1.1 - Life Expectancy The average life expectancy y of a...Ch. 1.1 - 41. Cigarette Consumption The worldwide...Ch. 1.1 - 42. Ecotourism Income In a certain developing...Ch. 1.1 - Insurance Rates Yearly car insurance rates have...Ch. 1.1 - Simple Interest If $1000 is deposited at 3% simple...Ch. 1.1 - 45. College Freshmen The percentage, y, of college...Ch. 1.1 - College Freshmen The percentage, y, of college...Ch. 1.1 - College Tuition Average tuition (including room...Ch. 1.1 - 48. Bachelor’s Degrees The number of bachelor’s...Ch. 1.1 - 49. Find an equation of the line having...Ch. 1.1 - Find an equation of the line having x-intercept...Ch. 1.1 - Find an equation of the line having y-intercept...Ch. 1.1 - Find an equation of the line having x-intercept...Ch. 1.1 - 53. What is the equation of the x-axis?
Ch. 1.1 - 54. Can a line other than the x-axis have more...Ch. 1.1 - 55. What is the general form of the equation of a...Ch. 1.1 - What is the general form of the equation of a line...Ch. 1.1 - In Exercises 5760, find a general form of the...Ch. 1.1 - In Exercises 5760, find a general form of the...Ch. 1.1 - In Exercises 5760, find a general form of the...Ch. 1.1 - In Exercises 57–60, find a general form of the...Ch. 1.1 - Show that the straight line with x-intercept (a,0)...Ch. 1.1 - Use the result of Exercise 61 to find a general...Ch. 1.1 - In Exercises 6370, give the equation of a line...Ch. 1.1 - In Exercises 6370, give the equation of a line...Ch. 1.1 - In Exercises 63–70, give the equation of a line...Ch. 1.1 - In Exercises 63–70, give the equation of a line...Ch. 1.1 - In Exercises 63–70, give the equation of a line...Ch. 1.1 - In Exercises 6370, give the equation of a line...Ch. 1.1 - In Exercises 63–70, give the equation of a line...Ch. 1.1 - In Exercises 6370, give the equation of a line...Ch. 1.1 - 71. The lines with equations and have the same...Ch. 1.1 - The lines with equations 6x3y=9 and y=4x+b have...Ch. 1.1 - In Exercises 7376, (a) graph the line, (b) use the...Ch. 1.1 - In Exercises 73–76, (a) graph the line, (b) use...Ch. 1.1 - In Exercises 7376, (a) graph the line, (b) use the...Ch. 1.1 - In Exercises 73–76, (a) graph the line, (b) use...Ch. 1.1 - In Exercises 77 and 78, determine an appropriate...Ch. 1.1 - In Exercises 77 and 78, determine an appropriate...Ch. 1.2 - Suppose that the revenue y from selling x units of...Ch. 1.2 - Suppose that the revenue y from selling x units of...Ch. 1.2 - In Exercises 1–6, find the slope of the line...Ch. 1.2 - In Exercises 1–6, find the slope of the line...Ch. 1.2 - In Exercises 1–6, find the slope of the line...Ch. 1.2 - In Exercises 16, find the slope of the line having...Ch. 1.2 - In Exercises 16, find the slope of the line having...Ch. 1.2 - In Exercises 1–6, find the slope of the line...Ch. 1.2 - In Exercises 710, plot each pair of points, draw...Ch. 1.2 - In Exercises 710, plot each pair of points, draw...Ch. 1.2 - In Exercises 7–10, plot each pair of points, draw...Ch. 1.2 - In Exercises 710, plot each pair of points, draw...Ch. 1.2 - What is the slope of any line parallel to the...Ch. 1.2 - Why doesnt it make sense to talk about the slope...Ch. 1.2 - In Exercises 1316, graph the given linear equation...Ch. 1.2 - In Exercises 13–16, graph the given linear...Ch. 1.2 - In Exercises 1316, graph the given linear equation...Ch. 1.2 - In Exercises 1316, graph the given linear equation...Ch. 1.2 - In Exercises 17–24, find the equation of line...Ch. 1.2 - In Exercises 17–24, find the equation of line...Ch. 1.2 - In Exercises 17–24, find the equation of line...Ch. 1.2 - In Exercises 1724, find the equation of line LCh. 1.2 - In Exercises 17–24, find the equation of line...Ch. 1.2 - In Exercises 17–24, find the equation of line...Ch. 1.2 - Prob. 23ECh. 1.2 - Prob. 24ECh. 1.2 - In Exercises 25–28, give the slope–intercept form...Ch. 1.2 - Prob. 26ECh. 1.2 - In Exercises 2528, give the slopeintercept form of...Ch. 1.2 - In Exercises 2528, give the slopeintercept form of...Ch. 1.2 - 29. Find the equation of the line passing through...Ch. 1.2 - 30. Find the equation of the line passing through...Ch. 1.2 - 31. Find the y-intercept of the line passing...Ch. 1.2 - 32. Find the y-intercept of the line passing...Ch. 1.2 - 33. Find the equation of the line passing through ...Ch. 1.2 - Find the equation of the line passing through the...Ch. 1.2 -
35. Cost Curve A manufacturer has fixed costs...Ch. 1.2 - Demand Curve The price p that must be set in order...Ch. 1.2 - 37. Boiling Point of Water At sea level, water...Ch. 1.2 - Cricket Chirps Biologists have found that the...Ch. 1.2 - Prob. 39ECh. 1.2 - Exercises 4042 are related. Cost Equation Suppose...Ch. 1.2 - Exercises 40–42 are related.
41. Revenue Equation...Ch. 1.2 - Exercises 4042 are related. Profit Equation...Ch. 1.2 - Prob. 43ECh. 1.2 - Cash Reserves A corporation receives payment for a...Ch. 1.2 - 45. Weekly Pay A furniture salesperson earns $220...Ch. 1.2 - 46. Weekly Pay A salesperson’s weekly pay depends...Ch. 1.2 - In Exercises 47–58, find an equation for each of...Ch. 1.2 - In Exercises 47–58, find an equation for each of...Ch. 1.2 - In Exercises 4758, find an equation for each of...Ch. 1.2 - In Exercises 4758, find an equation for each of...Ch. 1.2 - In Exercises 47–58, find an equation for each of...Ch. 1.2 - In Exercises 4758, find an equation for each of...Ch. 1.2 - In Exercises 47–58, find an equation for each of...Ch. 1.2 - In Exercises 4758, find an equation for each of...Ch. 1.2 - In Exercises 4758, find an equation for each of...Ch. 1.2 - In Exercises 47–58, find an equation for each of...Ch. 1.2 - Prob. 57ECh. 1.2 - Prob. 58ECh. 1.2 - Prob. 59ECh. 1.2 - In each of Exercises 5962, we specify a line by...Ch. 1.2 - Prob. 61ECh. 1.2 - Prob. 62ECh. 1.2 - Prob. 63ECh. 1.2 - Prob. 64ECh. 1.2 - Prob. 65ECh. 1.2 - Prob. 66ECh. 1.2 - Prob. 67ECh. 1.2 - Prob. 68ECh. 1.2 - Prob. 69ECh. 1.2 - Prob. 70ECh. 1.2 - Prob. 71ECh. 1.2 - 72. Dating of Artifacts An archaeologist dates a...Ch. 1.2 - Prob. 73ECh. 1.2 - 74. College Enrollments Two-year college...Ch. 1.2 - Gas Mileage A certain car gets 25 miles per gallon...Ch. 1.2 - 76. Home Health Aid Jobs According to the U.S....Ch. 1.2 - Prob. 77ECh. 1.2 - Pizza Stores According to Pizza Marketing...Ch. 1.2 - 79. Super Bowl Commercials The average cost of a...Ch. 1.2 - 80. Straight-Line Depreciation A multi-function...Ch. 1.2 - Supply Curve Suppose that 5 million tons of apples...Ch. 1.2 - Demand Curve Suppose that 5 million tons of apples...Ch. 1.2 - Show that the points (1,3),(2,4),and(3,1) are not...Ch. 1.2 - For what value of k will the three points...Ch. 1.2 - Find the value of a for which the line through the...Ch. 1.2 - 86. Rework Exercise 85, where the word parallel is...Ch. 1.2 - Prove the parallel property. [Hint: If...Ch. 1.2 - Prob. 88ECh. 1.2 - Prob. 89ECh. 1.2 - Prob. 90ECh. 1.2 - 91. Costs and Revenue A T-shirt company has fixed...Ch. 1.2 - 92. Costs and Revenue A company produces a single...Ch. 1.2 - Demand and Revenue Suppose that the quantity q of...Ch. 1.2 - 94. Demand and Revenue Suppose that the number n...Ch. 1.2 - Setting a Price During 2015, a manufacturer...Ch. 1.2 - 96. Setting a Price Rework Exercise 95 with a 2015...Ch. 1.2 - 97. Graph the three lines together, and then...Ch. 1.2 - Prob. 98ECh. 1.2 - Prob. 99ECh. 1.2 - Prob. 100ECh. 1.2 - Prob. 101ECh. 1.3 - Figure 9 shows a type of polygon that plays a...Ch. 1.3 - Figure 9 shows a type of polygon that plays a...Ch. 1.3 - Figure 9 shows a type of polygon that plays a...Ch. 1.3 - In Exercises 16, find the point of intersection of...Ch. 1.3 - In Exercises 16, find the point of intersection of...Ch. 1.3 - In Exercises 16, find the point of intersection of...Ch. 1.3 - In Exercises 1–6, find the point of intersection...Ch. 1.3 - In Exercises 16, find the point of intersection of...Ch. 1.3 - Prob. 6ECh. 1.3 - 7. Does satisfy the following system of linear...Ch. 1.3 - Does (12,4) satisfy the following system of linear...Ch. 1.3 - In Exercises 9-12, solve the systems of linear...Ch. 1.3 - In Exercises 9-12, solve the systems of linear...Ch. 1.3 - In Exercises 9-12, solve the systems of linear...Ch. 1.3 - In Exercises 9-12, solve the systems of linear...Ch. 1.3 - In Exercises 13–16, find the coordinates of the...Ch. 1.3 - In Exercises 13–16, find the coordinates of the...Ch. 1.3 - In Exercises 13–16, find the coordinates of the...Ch. 1.3 - In Exercises 1316, find the coordinates of the...Ch. 1.3 - Supply Curve The supply curve for a certain...Ch. 1.3 - 18. Demand Curve The demand curve for a certain...Ch. 1.3 - 19. Supply and Demand Suppose that supply and...Ch. 1.3 - Supply and Demand A discount book seller has...Ch. 1.3 - 21. Supply and Demand Suppose that the demand...Ch. 1.3 - Prob. 22ECh. 1.3 - Temperature Conversion The formula for converting...Ch. 1.3 - Prob. 24ECh. 1.3 - 25. Manufacturing A clothing store can purchase a...Ch. 1.3 - 26. Time Apportionment A plant supervisor must...Ch. 1.3 - Calling Card Options A calling card offers two...Ch. 1.3 - 28. Towing Fees Sun Towing Company charges $50...Ch. 1.3 - In Exercises 29 and 30, find the area of the...Ch. 1.3 - Prob. 30ECh. 1.3 - Prob. 31ECh. 1.3 - 32. Sales Determination An appliance store sells a...Ch. 1.3 - Prob. 33ECh. 1.3 - In Exercises 33-36, graph the lines and estimate...Ch. 1.3 - Prob. 35ECh. 1.3 - In Exercises 33-36, graph the lines and estimate...Ch. 1.4 - 1. Can a vertical distance be negative?
Ch. 1.4 - Under what condition will a vertical distance be...Ch. 1.4 - Suppose that the line y=3x+1 is used to fit the...Ch. 1.4 - 2. Suppose that the line is used to fit the four...Ch. 1.4 - 3. Find the sum-of-squares error E for the...Ch. 1.4 - Find the sum-of-squares error E for the...Ch. 1.4 - Complete Table 6, and find the values of m and b...Ch. 1.4 - 6. Complete Table 7, and find the values of m and...Ch. 1.4 - Consider the data points (1,2),(2,5),and(3,11)....Ch. 1.4 - 8. Consider the data points . Find the straight...Ch. 1.4 - 9. Consider the data points, and . Find the...Ch. 1.4 - Consider the data points (1,5),(2,7),(3,6), and...Ch. 1.4 - 11. Consider the data points and .
(a) Find the...Ch. 1.4 - Prob. 12ECh. 1.4 - According to Example 2, the sum-of-squares error...Ch. 1.4 - Prob. 14ECh. 1.4 - Fuel Economy The following table gives the city...Ch. 1.4 - 16. Pizzerias The following table gives the number...Ch. 1.4 - Lung cancer and Smoking The following table gives...Ch. 1.4 - Cigarette Use The percentage of college freshmen...Ch. 1.4 - 19. College Graduates Figure 15 gives the percent...Ch. 1.4 - Average College Costs Figure 16 gives the average...Ch. 1.4 - Life Expectancy The following table is an...Ch. 1.4 - Banking Two Harvard economists studied countries...Ch. 1.4 - 23. Consumer Price Index The following table gives...Ch. 1.4 - Greenhouse Gases Although greenhouse gases are...Ch. 1 - How do you determine the coordinates of a point in...Ch. 1 - 2. What is meant by the graph of an equation in x...Ch. 1 - 3. What is the y-intercept of a line? How do you...Ch. 1 - 4. What is the x-intercept of a line? How do you...Ch. 1 - Prob. 5FCCECh. 1 - Prob. 6FCCECh. 1 - Prob. 7FCCECh. 1 - Prob. 8FCCECh. 1 - Prob. 9FCCECh. 1 - Prob. 10FCCECh. 1 - Prob. 11FCCECh. 1 - What can you say about the slopes of perpendicular...Ch. 1 - Prob. 13FCCECh. 1 - Prob. 14FCCECh. 1 - What is the least-squares line approximation to a...Ch. 1 - 1. What is the equation of the y-axis?
Ch. 1 - Prob. 2RECh. 1 - Find the point of intersection of the pair of...Ch. 1 - Prob. 4RECh. 1 - Prob. 5RECh. 1 - Prob. 6RECh. 1 - Prob. 7RECh. 1 - Find the y-coordinate of the point having...Ch. 1 - Prob. 9RECh. 1 - Solve the system of linear equations....Ch. 1 - Prob. 11RECh. 1 - Cost of Moving The fee charged by a local moving...Ch. 1 - Are the points (1,2),(2,0), and (3,1) on the same...Ch. 1 - Prob. 14RECh. 1 - Prob. 15RECh. 1 - Prob. 16RECh. 1 - Prob. 17RECh. 1 - Prob. 18RECh. 1 - Prob. 19RECh. 1 - Prob. 20RECh. 1 - Prob. 21RECh. 1 - 22. Supply and Demand Consider the following four...Ch. 1 - Prob. 23RECh. 1 - Prob. 24RECh. 1 - Car Rentals One-day car rentals cost $50 plus 10...Ch. 1 - 26. Inflation In 2003, bacon cost an average of...Ch. 1 - Medical assistant Jobs According to the U.S....Ch. 1 - Prob. 28RECh. 1 - Prob. 29RECh. 1 - Prob. 30RECh. 1 - Prob. 31RECh. 1 - 32. Life Expectancy The following table gives the...Ch. 1 - Prob. 33RECh. 1 - Prob. 34RECh. 1 - Prob. 35RECh. 1 - Prob. 36RECh. 1 - 37. When is the x-intercept of a line the same as...Ch. 1 - 38. Suppose that you have found the least-squares...Ch. 1 - Does every line have an x-intercept? A...Ch. 1 - 40. Consider the line having the slope–intercept...Ch. 1 - Break-Even Analysis
We discussed linear demand...Ch. 1 - Break-Even Analysis We discussed linear demand...Ch. 1 - Break-Even Analysis
We discussed linear demand...Ch. 1 - Break-Even Analysis We discussed linear demand...Ch. 1 - Break-Even Analysis
We discussed linear demand...Ch. 1 - Break-Even Analysis
We discussed linear demand...Ch. 1 - Break-Even Analysis We discussed linear demand...Ch. 1 - Break-Even Analysis
We discussed linear demand...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Answersarrow_forwardWhat is a solution to a differential equation? We said that a differential equation is an equation that describes the derivative, or derivatives, of a function that is unknown to us. By a solution to a differential equation, we mean simply a function that satisfies this description. 2. Here is a differential equation which describes an unknown position function s(t): ds dt 318 4t+1, ds (a) To check that s(t) = 2t2 + t is a solution to this differential equation, calculate you really do get 4t +1. and check that dt' (b) Is s(t) = 2t2 +++ 4 also a solution to this differential equation? (c) Is s(t)=2t2 + 3t also a solution to this differential equation? ds 1 dt (d) To find all possible solutions, start with the differential equation = 4t + 1, then move dt to the right side of the equation by multiplying, and then integrate both sides. What do you get? (e) Does this differential equation have a unique solution, or an infinite family of solutions?arrow_forwardthese are solutions to a tutorial that was done and im a little lost. can someone please explain to me how these iterations function, for example i Do not know how each set of matrices produces a number if someine could explain how its done and provide steps it would be greatly appreciated thanks.arrow_forward
- Q1) Classify the following statements as a true or false statements a. Any ring with identity is a finitely generated right R module.- b. An ideal 22 is small ideal in Z 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 A module M 0 is called directly indecomposable if and only if 0 and M are the only direct summands of M f. A monomorphism a: M-N is said to split if and only if Ker(a) is a direct- summand in M & Z₂ contains no minimal submodules h. Qz is a finitely generated module i. Every divisible Z-module is injective j. Every free module is a projective module Q4) Give an example and explain your claim in each case a) A module M which has two composition senes 7 b) A free subset of a modale c) A free module 24 d) A module contains a direct summand submodule 7, e) A short exact sequence of modules 74.arrow_forward************* ********************************* 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.arrow_forwardProve that Σ prime p≤x p=3 (mod 10) 1 Ρ = for some constant A. log log x + A+O 1 log x "arrow_forward
- Prove that, for x ≥ 2, d(n) n2 log x = B ― +0 X (금) n≤x where B is a constant that you should determine.arrow_forwardProve that, for x ≥ 2, > narrow_forwardI need diagram with solutionsarrow_forwardT. 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_forward1 2 21. For the matrix A = 3 4 find AT (the transpose of A). 22. Determine whether the vector @ 1 3 2 is perpendicular to -6 3 2 23. If v1 = (2) 3 and v2 = compute V1 V2 (dot product). .arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
HOW TO FIND DETERMINANT OF 2X2 & 3X3 MATRICES?/MATRICES AND DETERMINANTS CLASS XII 12 CBSE; Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=bnaKGsLYJvQ;License: Standard YouTube License, CC-BY
What are Determinants? Mathematics; Author: Edmerls;https://www.youtube.com/watch?v=v4_dxD4jpgM;License: Standard YouTube License, CC-BY