All Matches

Solution Library

Expert Answer

Textbooks

Search Textbook questions, tutors and Books

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Tutors
Study Help
Ask a Question

Search
Sign In
Register

study help
mathematics
linear algebra

Questions and Answers of Linear Algebra

Use the pie chart of a monthly entertainment budget.Entertainment Budgeta. Suppose $600 was budgeted. Determine the exact amount for each category.b. Suppose $72 was budgeted. What would be the total
Use the pie chart of a person's monthly income.a. Suppose the total monthly income is $5,800. Determine the amounts in each income category.b. Suppose the income from the secondary job was $1,225.
Rachel's health-related budget is as follows: The percentage budgeted for health insurance is four times the percentage for health club dues. The percentage budgeted for prescriptions is equal to
Construct a pie chart that shows the following transportation-related expenses: Fuel: $240; Insurance: $80; Public transportation: $200; Parking garage: $120; Repairs: $160.
Examine the following bar graph that shows budgeted monthly utility expenses for a one-year period.Utility Budgeta. In which months was the same amount budgeted?b. What is the total annual amount
Construct a bar graph for Jason's transportation budget expenses.
Explain how the quote can be interpreted in light of what you learned.Use the table below for Exercises 2 and 3.
Create a year-long budget for Laura as on page 515.In page 515
Add row 43 to your matrix from Exercise 9. Calculate each month's total expenses.In Exercise 9a. Draw a line graph to chart Laura's monthly budgeted expenses. Include horizontal lines to indicate the
Marina's monthly liabilities and assets are as shown in the table.a. Find Marina's debt-to-income ratio. Express that ratio as a percent.b. How would you categorize her debt-to-income ratio?
The Larsons use the average of six months as their budget starting point in each category. Find each average.
The Larsons (from Exercise 2) decided they would not use the September amounts, when they were on vacation, nor the December amounts, when cousins stayed with them. Assume the chart is a spreadsheet
Bob Forrester is retired and owns a home. He has these assets and liabilities.a. Calculate Bob's net worth.b. Two years ago, Bob's net worth was $650,000. Last year, his net worth as $740,500. What
The Consumer Credit Counseling Service suggests that the monthly food budget be between 15-30% of income.a. What is Laura's total monthly food bill including dining out? b. What percent of her income
Examine Laura's non-monthly expenses.a. Which month has the greatest expenses?b. How might Laura prepare for those expenses?
Use a cash flow template to construct a cash flow plan for Laura. What is her monthly cash flow?
Create a frequency budget for Laura as on page 513. Although her food, fuel, dining out, and entertainment expenses were listed monthly for the cash flow, they should be considered weekly expenses
Create spreadsheet for the frequency budget in Exercise 8.In Exercise 8
Jessica pays health, car, home, and life insurance over the course of a year. The chart below indicates her monthly insurance budget expenses. Create a bar graph to chart these expenses.
A pay phone at a railroad station charges $0.55 for the first five minutes (or part of) and $0.25 for each extra minute (or part of). Express the cost c(m) of an m-minute phone call as a piecewise
Phone-Phriends charges $37 for a text-message plan with 400 text messages included. If the customer goes over the 400 messages, the cost is $0.12 per text message. They have an unlimited plan which
A local cable TV/Internet/phone provider charges new customers $90 for all three services, per month, for the first year under their 90 NOW promotion. Alice normally pays $59 for her monthly home
Kalani has these monthly liabilities: rent $879, car payment $315, credit card payment $102. She has an annual income of $96,448. What is her debt-to-income ratio, expressed as a percent?
Leonard works as a waiter in an upscale city restaurant. He makes a very good salary plus tips. His monthly income varies based upon the nights he works. His quarterly dividend checks and interest
The pie chart shows a monthly utility budget.a. Suppose that $800 was budgeted for the month. Determine the exact amount for each category.b. Suppose that $117 was budgeted for water.What would be
Under her Dinner budget category, Diane allocated $600 per month for eating in and dining out. She figures that eating in will cost her approximately $8 and dining out will cost her approximately
Use the budget information for Nelson Shapiro for Exercise.
Create a frequency budget plan for Nelson. Although his food, fuel, dining out, and entertainment expenses were listed as monthly for the cash flow, they should be considered as weekly expenses here.
Draw the following vectors in standard position in R2:
Compute the indicated vectors. a. 2a + 3c b. 3b - 2c + d
Find the components of the vectors u, v, u + v, and u - v, where u and v are as shown in Figure 1 .23.
In Figure 1 .24, A, B, C, D, E, and F are the vertices of a regular hexagon centered at the origin.Express each of the following vectors in terms of
In Exercises 1 5 and 1 6, simplify the given vector expression. Indicate which properties in Theorem 1. 1 you use. a. 2(a - 3b) + 3 (2b + a) b. - 3(a - c) + 2(a + 2b) + 3(c - b)
In Exercises a and b, solve for the vector x in terms of the vectors a and b. a. x - a = 2(x - 2a) b. x + 2a - b = 3(x + a) - 2(2a - b)
In Exercises a and b, draw the coordinate axes relative to u and v and locate w.a.b.
Draw the vectors in Exercise 1 with their tails at the point (2, - 3).
In Exercises a and b, draw the standard coordinate axes on the same diagram as the axes relative to u and v. Use these to find w as a linear combination of u and v.a.b.
Draw diagrams to illustrate properties (d) and (e) of Theorem 1. 1.
Give algebraic proofs of properties (d) through (g) of Theorem 1. 1.
In Exercises 1-4, u and v are binary vectors. Find u + v in each casea.b. c. u = [1 , 0, 1 , 1] , v = [1, 1 , 1, 1] d. u = [1 , 1, 0, 1, 0] , v = [0, 1, 1 , 1, 0]
Write out the addition and multiplication tables for Z4.
Draw the following vectors in standard position in R3: (a) a = [0, 2, 0] (b) b = [3, 2, l] (c) c = [l , - 2, l] (d) d = [- 1, - 1 , - 2]
Write out the addition and multiplication tables for Zs.
Perform the indicated calculations. a. 2 + 2 + 2 in Z3 b. 2 · 2 · 2 in Z3 c. 2(2 + 1 + 2) in Z3 d. 3 + 1 + 2 + 3 in Z4 e. 2 · 3 · 2 in Z4
If the vectors in Exercise 3 are translated so that their heads are at the point (3, 2, 1), find the points that correspond to their tails. In exercise 3 (a) a = [0, 2, 0] (b) b = [3, 2, l] (c) c =
Solve the given equation or indicate that there is no solution. a. x + 3 = 2 in Zs b. x + 5 = 1 in Z6 c. 2x = 1 in Z3 d. 2x = 1 in Z4 e. 2x = 1 in Zs
(a) A = (1, - 1), B = (4, 2)(b) A = (0, - 2), B = (2, - 1)(c) A = (2, 3/2), B = (1/2, 3)(d) A = (1/3, 1/3), B = (1/6, 1/2)
(a) For which values of a does ax = 1 have a solution in Zs? (b) For which values of a does ax = 1 have a solution in Z6? (c) For which values of a and m does ax = 1 have a solution in Zm?
A hiker walks 4 km north and then 5 km northeast. Draw displacement vectors representing the hiker's trip and draw a vector that represents the hiker's net displacement from the starting point.
Compute the indicated vectors and also show how the results can be obtained geometrically. 1. a + b 2. b - c 3. d - c 4. a + d
In Exercises 1-3, determine whether the angle between u and v is acute, obtuse, or a right angle.1.2. 3. u = [4, 3, - 1] , v = [ l , - 1 , l]
Let A = (- 3, 2), B = (1, 0), and C = (4, 6). Prove that ∆ABC is a right-angled triangle.
Let A = (1, 1, - 1), B = (- 3, 2, - 2), and C = (2, 2, - 4). Prove that ∆ABC is a right-angled triangle.
Find the angle between a diagonal of a cube and an adjacent edge.
A cube has four diagonals. Show that no two of them are perpendicular.
A parallelogram has diagonals determined by the vectorsShow that the parallelogram is a rhombus (all sides of equal length) and determine the side length.
The rectangle ABCD has vertices at A = (1, 2, 3), B = (3, 6, - 2), and C = (0, 5, - 4). Determine the coordinates of vertex D.
An airplane heading due east has a velocity of 200 miles per hour. A wind is blowing from the north at 40 miles per hour. What is the resultant velocity of the airplane?
A boat heads north across a river at a rate of 4 miles per hour. If the current is flowing east at a rate of 3 miles per hour, find the resultant velocity of the boat.
Ann is driving a motorboat across a river that is 2 km wide. The boat has a speed of 20 km/h in still water, and the current in the river is flowing at 5 km/h. Ann heads out from one bank of the
Bert can swim at a rate of 2 miles per hour in still water. The current in a river is flowing at a rate of 1 mile per hour. If Bert wants to swim across the river to a point directly opposite, at
In Exercises a-b, find the projection of v onto u.a.b.
In Exercises 1 and 2, compute the area of the triangle with the given vertices using both methods.1. A = (1, - 1), B = (2, 2), C = (4, 0)2. A = (3, - 1, 4), B = (4, -2, 6), C = (5, 0, 2)Figure 1 .39
In exercise a and b, find all values of the scalar k for which the two vectors are orthogonal.a.b.
Describe all vectors v = [x y] that are orthogonal to u = [3 1].
Describe all vectorshat are orthogonal to
Under what conditions are the following true for vectors u and v in IR2 or IR3? (a) ||u + v|| = ||u|| + ||v|| (b) ||u + v|| = ||u|| - ||v||
Prove the stated property of distance between vectors. a. d(u, v) = d(v, u) for all vectors u and v b. d(u, w) ≤ d(u, v) + d(v, w) for all vectors u, v, and w c. d(u, v) = 0 if and only if u = v
Prove that u ∙ cv = c(u ∙ v) for all vectors u and v in Rn and all scalars c.
Prove that ||u - v|| ≥ ||u|| - ||v|| for all vectors u and v in Rn.
Suppose we know that u · v = u · w. Does it follow that v = w? If it does, give a proof that is valid in Rn; otherwise, give a counterexample (i.e., a specific set of vectors u, v, and w for which
Prove that (u + v) · (u - v) = ||u||2 - ||v||2 for all vectors u and v in Rn.
(a) Prove that ||u + v||2 + ||u - v||2 = 2||u||2 + 2||v||2 for all vectors u and v in Rn. (h) Draw a diagram showing u, v, u + v, and u - v in IR2 and use (a) to deduce a result about parallelograms.
Prove that u · v = - 1/4 ||u + v||2 - 1/4 ||u - v||2 for all vectors u and v in Rn.
(a) Prove that ||u + v|| = ||u - v|| if and only if u and v are orthogonal. (b) Draw a diagram showing u, v, u + v, and u - v in IR2 and use (a) to deduce a result about parallelograms.
(a) Prove that u + v and u - v are orthogonal in Rn if and only if ||u|| = ||v||. (b) Draw a diagram showing u, v, u + v, and u - v in IR2 and use (a) to deduce a result about parallelograms.
If ||u|| = 2, ||v|| = √3, and u · v = 1, find || u + v||.
(a) Prove that if u is orthogonal to both v and w, then u is orthogonal to v + w. (b) Prove that if u is orthogonal to both v and w, then u is orthogonal to sv + tw for all scalars s and t.
Prove that u is orthogonal to v - proju(v) for all vectors u and v in Rn, where u ≠ 0.
(a) Prove that proju(proju(v)) = proju(v).(b) Prove that proju(v - proju(v)) = 0.(c) Explain (a) and (b) geometrically.
The Cauchy-Schwarz Inequality |u · v| ‰¤ ||u|| ||v|| is equivalent to the inequality we get by squaring both sides: (u · v)2 ‰¤ ||u||2 ||v||2(a)Prove this
Figure 1 .40 shows that, in IR2 or IR3, || proju (v) | ‰¤ ||v||.(a) Prove that this inequality is true in general. (b) Prove that the inequality || proju (v) || ‰¤ || v || is
Use the fact that proju(v) = c u for some scalar c, together with Figure 1.41, to find c and thereby derive the formula for proju(v).
Using mathematical induction, prove the following generalization of the Triangle Inequality: ||v1 + v2 + ∙∙∙∙ + vn || ≤ || v1 || + || v2 || + ∙∙∙ + || vn || for all n ≥ 1
In Exercises 1 and 2, write the equation of the line passing through P with normal vector n in (a) normal form and (b) general form.1.2.
In Exercises 1 and 2, give the vector equation of the line passing through P and Q. 1. P = (1, - 2), Q = (3, 0) 2. P = (0, 1, - 1), Q = (- 2, 1, 3)
In Exercises 1 and 2, give the vector equation of the plane passing through P, Q, and R. 1. P = (1, 1, 1), Q = (4, 0, 2), R = (0, 1, - 1) 2. P = (1, 1, 0), Q = (1, 0, 1), R = (0, 1, 1)
Find parametric equations and an equation in vector form for the lines in R2 with the following equations: (a) y = 3x - 1 (b) 3x + 2y = 5
Consider the vector equation x = p + t(q - p) , where p and q correspond to distinct points P and Q in R2 or R3. (a) Show that this equation describes the line segment PQ as t varies from 0 to 1. (b)
Suggest a "vector proof" of the fact that, in R2, two lines with slopes m1 and m2 are perpendicular if and only if m1 m2 = - 1.
The line e passes through the point P = (1, - 1, 1) and has direction vectorFor each of the following planes P, determine whether „“ and P are parallel, perpendicular, or neither: (a) 2x +
The plane P1 has the equation 4x - y + 5z = 2. For each of the planes P1 in Exercise 18, determine whether P1 and P are parallel, perpendicular, or neither. In exercise 18 (a) 2x + 3y - z = 1 (b) 4x
Find the vector form of the equation of the line in R2 that passes through P = (2, - 1) and is perpendicular to the line with general equation 2x - 3y = 1.
Find the vector form of the equation of the line in R2 that passes through P = (2, - 1) and is parallel to the line with general equation 2x - 3y = 1.
Find the vector form of the equation of the line in R3 that passes through P = (- 1, 0, 3) and is perpendicular to the plane with general equation x - 3y + 2z = 5
Find the vector form of the equation of the line in IR3 that passes through P = (- 1, 0, 3) and is parallel to the line with parametric equations x = 1 - t y = 2 + 3t z = - 2 - t
Find the normal form of the equation of the plane that passes through P = (0, - 2, 5) and is parallel to the plane with general equation 6x - y + 2z = 3.
A cube has vertices at the eight points (x, y, z), where each of x, y, and z is either 0 or 1. (a) Find the general equations of the planes that determine the six faces (sides) of the cube. (b) Find
Find the equation of the set of all points that are equidistant from the points P = (1, 0, - 2) and Q = (5, 2, 4).
In Exercises 1 and 2, find the distance from the point Q to the line „“.1. Q = (2, 2), „“ with equation2. Q = (0, 1, 0), „“ with equation

Showing 2100 - 2200 of 11890

First
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
Last

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Campus Ambassador

Company Info

Security
Copyrights
Privacy Policy
Terms & Condition
SolutionInn Fee
Scholarship

Services

Sitemap
Fun
Definitions
Become Tutor
Study Help Categories
Recent Questions
Expert Questions

Copyright © 2024 SolutionInn All Rights Reserved.

Get the SolutionInn - Study Help App