Intermediate Algebra
19th Edition
ISBN: 9780998625720
Author: Lynn Marecek
Publisher: OpenStax College
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Textbook Question
Chapter 2.3, Problem 2.60TI
Solve the formula
Expert Solution & Answer
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Check out a sample textbook solutionStudents have asked these similar questions
Let
2
A =
4
3
-4
0
1
(a) Show that v =
eigenvalue.
()
is an eigenvector of A and find the corresponding
(b) Find the characteristic polynomial of A and factorise it. Hint: the answer to (a)
may be useful.
(c) Determine all eigenvalues of A and find bases for the corresponding eigenspaces.
(d) Find an invertible matrix P and a diagonal matrix D such that P-¹AP = D.
(c) Let
6
0 0
A =
-10 4 8
5 1 2
(i) Find the characteristic polynomial of A and factorise it.
(ii) Determine all eigenvalues of A and find bases for the corresponding
eigenspaces.
(iii) Is A diagonalisable? Give reasons for your answer.
most 2, and let
Let P2 denote the vector space of polynomials of degree at
D: P2➡ P2
be the transformation that sends a polynomial p(t) = at² + bt+c in P2 to its derivative
p'(t)
2at+b, that is,
D(p) = p'.
(a) Prove that D is a linear transformation.
(b) Find a basis for the kernel ker(D) of the linear transformation D and compute its
nullity.
(c) Find a basis for the image im(D) of the linear transformation D and compute its
rank.
(d) Verify that the Rank-Nullity Theorem holds for the linear transformation D.
(e) Find the matrix representation of D in the standard basis (1,t, t2) of P2.
Chapter 2 Solutions
Intermediate Algebra
Ch. 2.1 - Determine whether the values are solutions to the...Ch. 2.1 - Determine whether the values are solutions to the...Ch. 2.1 - Solve: 2(m4)+3=1 .Ch. 2.1 - Solve: 5(a3)+5=10 .Ch. 2.1 - Solve: 13(6u+3)=7u .Ch. 2.1 - Solve: 23(9x12)=8+2x .Ch. 2.1 - Solve: 6(p3)7=5(4p+3)12 .Ch. 2.1 - Solve: 8(q+1)5=3(2q4)1 .Ch. 2.1 - Solve: 6[42(7y1)]=8(138y) .Ch. 2.1 - Solve: 12[15(4z1)]=3(24+11z) .
Ch. 2.1 - Classify the equation as a conditional equation,...Ch. 2.1 - Classify the equation as a conditional equation,...Ch. 2.1 - Classify the equation as a conditional equation,...Ch. 2.1 - Classify the equation as a conditional equation,...Ch. 2.1 - Classify the equation as a conditional equation,...Ch. 2.1 - Classify the equation as a conditional equation,...Ch. 2.1 - Solve: 14x+12=58 .Ch. 2.1 - Solve: 18x+12=14 .Ch. 2.1 - Solve: 7=12x+34x23x .Ch. 2.1 - Solve: 1=12u+14u23u .Ch. 2.1 - Solve: 15(n+3)=14(n+2) .Ch. 2.1 - Solve: 12(m4)=14(m7) .Ch. 2.1 - Solve: 3r+56+1=4r+33 .Ch. 2.1 - Solve: 2s+32+1=3s+24 .Ch. 2.1 - Solve: 0.25n+0.05(n+5)=2.95 .Ch. 2.1 - Solve: 0.10d+0.05(d5)=2.15 .Ch. 2.1 - In the following exercises, determine whether the...Ch. 2.1 - In the following exercises, determine whether the...Ch. 2.1 - In the following exercises, determine whether the...Ch. 2.1 - In the following exercises, determine whether the...Ch. 2.1 - In the following exercises, solve each linear...Ch. 2.1 - In the following exercises, solve each linear...Ch. 2.1 - In the following exercises, solve each linear...Ch. 2.1 - In the following exercises, solve each linear...Ch. 2.1 - In the following exercises, solve each linear...Ch. 2.1 - In the following exercises, solve each linear...Ch. 2.1 - In the following exercises, solve each linear...Ch. 2.1 - In the following exercises, solve each linear...Ch. 2.1 - In the following exercises, solve each linear...Ch. 2.1 - In the following exercises, solve each linear...Ch. 2.1 - In the following exercises, solve each linear...Ch. 2.1 - In the following exercises, solve each linear...Ch. 2.1 - In the following exercises, solve each linear...Ch. 2.1 - In the following exercises, solve each linear...Ch. 2.1 - In the following exercises, solve each linear...Ch. 2.1 - In the following exercises, solve each linear...Ch. 2.1 - In the following exercises, solve each linear...Ch. 2.1 - In the following exercises, solve each linear...Ch. 2.1 - In the following exercises, solve each linear...Ch. 2.1 - 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In the following exercises, classify each equation...Ch. 2.1 - In the following exercises, classify each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - 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Using your own words, list the steps in the...Ch. 2.1 - Explain why you should simplify both sides of an...Ch. 2.1 - What is the first step you take when solving the...Ch. 2.1 - If an equation has several fractions, how does...Ch. 2.1 - If an equation has fractions only on one side, why...Ch. 2.1 - For the equation 0.35x+2.1=3.85 , how do you clear...Ch. 2.2 - Guillermo bought textbooks and notebooks at the...Ch. 2.2 - Gerry worked Sudoku puzzles and crossword puzzles...Ch. 2.2 - The sum of four times a number and two is...Ch. 2.2 - The sum of three times a number and seven is...Ch. 2.2 - The sum of two numbers is negative twenty-three....Ch. 2.2 - The sum of two numbers is negative eighteen. One...Ch. 2.2 - Find three consecutive integers whose sum is 96 .Ch. 2.2 - Find three consecutive integers whose sum is 36 .Ch. 2.2 - Find three consecutive even integers whose sum is...Ch. 2.2 - Find three consecutive even integers whose sum is...Ch. 2.2 - According to the National Automobile Dealers...Ch. 2.2 - US Census data shows that the median price of new...Ch. 2.2 - Translate and solve: (a) What number is 45% of 80?...Ch. 2.2 - Translate and solve: (a) What number is 55% of 60?...Ch. 2.2 - One serving of wheat square cereal has 7 grams of...Ch. 2.2 - One serving of rice cereal has 190 mg of sodium,...Ch. 2.2 - Mitzi received some gourmet brownies as a gift....Ch. 2.2 - The mix Ricardo plans to use to make brownies says...Ch. 2.2 - Find the percent change. (Round to the nearest...Ch. 2.2 - Find the percent change. (Round to the nearest...Ch. 2.2 - Find (a) the amount of mark-up and (b) the list...Ch. 2.2 - Find (a) the amount of mark-up and (b) the list...Ch. 2.2 - Nathaly deposited $12,500 in her bank account...Ch. 2.2 - Susana invested a principal of $36,000 in her bank...Ch. 2.2 - Jim lent his sister $5,000 to help her buy a...Ch. 2.2 - Loren lent his brother $3,000 to help him buy a...Ch. 2.2 - Eduardo noticed that his new car loan papers...Ch. 2.2 - In five years, Gloria’s bank account earned $2,400...Ch. 2.2 - List five positive thoughts you can say to...Ch. 2.2 - List five negative thoughts that you have said to...Ch. 2.2 - In the following exercises, solve using the...Ch. 2.2 - In the following exercises, solve using the...Ch. 2.2 - In the following exercises, solve using the...Ch. 2.2 - In the following exercises, solve using the...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, solve each number word...Ch. 2.2 - In the following exercises, translate and solve....Ch. 2.2 - In the following exercises, translate and solve....Ch. 2.2 - In the following exercises, translate and solve....Ch. 2.2 - In the following exercises, translate and solve....Ch. 2.2 - In the following exercises, solve. 121. Geneva...Ch. 2.2 - In the following exercises, solve. 122. When Hiro...Ch. 2.2 - In the following exercises, solve. 123. One...Ch. 2.2 - In the following exercises, solve. 124. One...Ch. 2.2 - In the following exercises, solve. 125. A bacon...Ch. 2.2 - In the following exercises, solve. 126. A grilled...Ch. 2.2 - In the following exercises, solve. 127. The...Ch. 2.2 - In the following exercises, solve. 128. The...Ch. 2.2 - In the following exercises, solve. 129. Emma gets...Ch. 2.2 - In the following exercises, solve. 130. Dimple...Ch. 2.2 - In the following exercises, solve. 131. Tamanika...Ch. 2.2 - In the following exercises, solve. 132. Ayodele...Ch. 2.2 - In the following exercises, solve. 133. Annual...Ch. 2.2 - In the following exercises, solve. 134. The price...Ch. 2.2 - In the following exercises, solve. 135. A grocery...Ch. 2.2 - In the following exercises, solve. 136. The price...Ch. 2.2 - In the following exercises, solve. 137. Hernando’s...Ch. 2.2 - In the following exercises, solve. 138. In ten...Ch. 2.2 - In the following exercises, find (a) the amount of...Ch. 2.2 - In the following exercises, find (a) the amount of...Ch. 2.2 - In the following exercises, find (a) the amount of...Ch. 2.2 - In the following exercises, find (a) the amount of...Ch. 2.2 - In the following exercises, find (a) the amount of...Ch. 2.2 - In the following exercises, find (a) the amount of...Ch. 2.2 - In the following exercises, find (a) the amount of...Ch. 2.2 - In the following exercises, find (a) the amount of...Ch. 2.2 - In the following exercises, solve. 147. Casey...Ch. 2.2 - In the following exercises, solve. 148. Terrence...Ch. 2.2 - In the following exercises, solve. 149. Robin...Ch. 2.2 - In the following exercises, solve. 150. Carleen...Ch. 2.2 - In the following exercises, solve. 151. Hilaria...Ch. 2.2 - In the following exercises, solve. 152. Kenneth...Ch. 2.2 - In the following exercises, solve. 153. Lebron...Ch. 2.2 - In the following exercises, solve. 154. Pablo...Ch. 2.2 - In the following exercises, solve. 155. In 10...Ch. 2.2 - In the following exercises, solve. 156. In 25...Ch. 2.2 - In the following exercises, solve. 157. Joshua’s...Ch. 2.2 - In the following exercises, solve. 158. Margaret’s...Ch. 2.2 - Tipping At the campus coffee cart, a medium coffee...Ch. 2.2 - Tipping Four friends went out to lunch and the...Ch. 2.2 - What has been your past experience solving word...Ch. 2.2 - Without solving the problem “44 is 80% of what...Ch. 2.2 - After returning from vacation, Alex said he should...Ch. 2.2 - Because of road construction in one city,...Ch. 2.3 - Use the formula A=12bh to solve for b.Ch. 2.3 - Use the formula A=12bh to solve for h.Ch. 2.3 - Solve the formula F=95C+32 for C.Ch. 2.3 - Solve the formula A=12h(b+B) for b.Ch. 2.3 - Solve the formula A=P+Prt for t.Ch. 2.3 - Solve the formula A=P+Prt for r.Ch. 2.3 - Solve the formula 4x+7y=9 for y.Ch. 2.3 - Solve the formula 5x+8y=1 for y.Ch. 2.3 - The area of a triangular church window is 90...Ch. 2.3 - A triangular tent door has area 15 square feet....Ch. 2.3 - The measure of one angle of a right triangle is 50...Ch. 2.3 - The measure of one angle of a right triangle is 30...Ch. 2.3 - Use the Pythagorean Theorem to find the length of...Ch. 2.3 - Use the Pythagorean Theorem to find the length of...Ch. 2.3 - The length of a rectangle is seven more than twice...Ch. 2.3 - The width of a rectangle is eight yards less than...Ch. 2.3 - One side of a triangle is seven inches more than...Ch. 2.3 - One side of a triangle is three feet less than the...Ch. 2.3 - The perimeter of a rectangular swimming pool is...Ch. 2.3 - The length of a rectangular garden is 30 yards...Ch. 2.3 - John puts the base of a 13-foot ladder five feet...Ch. 2.3 - Randy wants to attach a 17-foot string of lights...Ch. 2.3 - In the following exercises, solve the given...Ch. 2.3 - In the following exercises, solve the given...Ch. 2.3 - In the following exercises, solve the given...Ch. 2.3 - In the following exercises, solve the given...Ch. 2.3 - In the following exercises, solve the given...Ch. 2.3 - In the following exercises, solve the given...Ch. 2.3 - In the following exercises, solve the given...Ch. 2.3 - In the following exercises, solve the given...Ch. 2.3 - 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In the following exercises, use the Pythagorean...Ch. 2.3 - In the following exercises, use the Pythagorean...Ch. 2.3 - In the following exercises, use the Pythagorean...Ch. 2.3 - In the following exercises, use the Pythagorean...Ch. 2.3 - In the following exercises, use the Pythagorean...Ch. 2.3 - In the following exercises, use the Pythagorean...Ch. 2.3 - In the following exercises, use the Pythagorean...Ch. 2.3 - In the following exercises, solve using a geometry...Ch. 2.3 - In the following exercises, solve using a geometry...Ch. 2.3 - In the following exercises, solve using a geometry...Ch. 2.3 - In the following exercises, solve using a geometry...Ch. 2.3 - In the following exercises, solve using a geometry...Ch. 2.3 - In the following exercises, solve using a geometry...Ch. 2.3 - In the following exercises, solve using a geometry...Ch. 2.3 - In the following exercises, solve using a geometry...Ch. 2.3 - In the following exercises, solve using a geometry...Ch. 2.3 - In the following exercises, solve using a geometry...Ch. 2.3 - 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Approximate...Ch. 2.3 - In the following exercises, solve. Approximate...Ch. 2.3 - In the following exercises, solve. Approximate...Ch. 2.3 - In the following exercises, solve. Approximate...Ch. 2.3 - Converting temperature While on a tour in Greece,...Ch. 2.3 - Converting temperature Yon was visiting the United...Ch. 2.3 - Christa wants to put a fence around her triangular...Ch. 2.3 - Jose just removed the children’s play set from his...Ch. 2.3 - If you need to put tile on your kitchen floor, do...Ch. 2.3 - If you need to put a fence around your backyard,...Ch. 2.3 - Look at the two figures below. (a) Which figure...Ch. 2.3 - Write a geometry word problem that relates to your...Ch. 2.4 - Jesse has $6.55 worth of quarters and nickels in...Ch. 2.4 - Elane has $7.00 total in dimes and nickels in her...Ch. 2.4 - Eric paid $19.88 for stamps. The number of 49-cent...Ch. 2.4 - Kailee paid $14.74 for stamps. The number of...Ch. 2.4 - During her shift at the museum ticket booth, Leah...Ch. 2.4 - Galen sold 810 tickets for his church’s carnival...Ch. 2.4 - Orlando is mixing nuts and cereal squares to make...Ch. 2.4 - Becca wants to mix fruit juice and soda to make a...Ch. 2.4 - An express train and a local train leave...Ch. 2.4 - Jeromy can drive from his house in Cleveland to...Ch. 2.4 - Christopher and his parents live 115 miles apart....Ch. 2.4 - Ashley goes to college in Minneapolis, 234 miles...Ch. 2.4 - Pierre and Monique leave their home in Portland at...Ch. 2.4 - Thanh and Nhat leave their office in Sacramento at...Ch. 2.4 - Suzy takes 50 minutes to hike uphill from the...Ch. 2.4 - Llewyn takes 45 minutes to drive his boat upstream...Ch. 2.4 - Hamilton loves to travel to Las Vegas, 255 miles...Ch. 2.4 - Phuong left home on his bicycle at 10:00. He rode...Ch. 2.4 - In the following exercises, solve each coin word...Ch. 2.4 - In the following exercises, solve each coin word...Ch. 2.4 - In the following exercises, solve each coin word...Ch. 2.4 - In the following exercises, solve each coin word...Ch. 2.4 - In the following exercises, solve each coin word...Ch. 2.4 - In the following exercises, solve each coin word...Ch. 2.4 - In the following exercises, solve each coin word...Ch. 2.4 - In the following exercises, solve each coin word...Ch. 2.4 - In the following exercises, solve each ticket or...Ch. 2.4 - In the following exercises, solve each ticket or...Ch. 2.4 - In the following exercises, solve each ticket or...Ch. 2.4 - In the following exercises, solve each ticket or...Ch. 2.4 - In the following exercises, solve each ticket or...Ch. 2.4 - In the following exercises, solve each ticket or...Ch. 2.4 - In the following exercises, solve each ticket or...Ch. 2.4 - In the following exercises, solve each ticket or...Ch. 2.4 - In the following exercises, solve each ticket or...Ch. 2.4 - In the following exercises, solve each ticket or...Ch. 2.4 - In the following exercises, solve each mixture...Ch. 2.4 - In the following exercises, solve each mixture...Ch. 2.4 - In the following exercises, solve each mixture...Ch. 2.4 - In the following exercises, solve each mixture...Ch. 2.4 - In the following exercises, solve each mixture...Ch. 2.4 - In the following exercises, solve each mixture...Ch. 2.4 - In the following exercises, solve each mixture...Ch. 2.4 - In the following exercises, solve. 268. Lilah is...Ch. 2.4 - In the following exercises, solve. 269. Kathy and...Ch. 2.4 - the following exercises, solve. 270. Two busses go...Ch. 2.4 - In the following exercises, solve. 271. A...Ch. 2.4 - In the following exercises, solve. 272. Saul drove...Ch. 2.4 - In the following exercises, solve. 273. Charlie...Ch. 2.4 - In the following exercises, solve. 274. Sisters...Ch. 2.4 - In the following exercises, solve. 275. Ethan and...Ch. 2.4 - In the following exercises, solve. 276. Elvira and...Ch. 2.4 - In the following exercises, solve. 277. DaMarcus...Ch. 2.4 - In the following exercises, solve. 278. Cindy and...Ch. 2.4 - In the following exercises, solve. 279. Matt and...Ch. 2.4 - In the following exercises, solve. 280. Two busses...Ch. 2.4 - In the following exercises, solve. 281. Two boats...Ch. 2.4 - In the following exercises, solve. 282. Lorena...Ch. 2.4 - In the following exercises, solve. 283. Julian...Ch. 2.4 - In the following exercises, solve. 284. Cassius...Ch. 2.4 - In the following exercises, solve. 285. It takes...Ch. 2.4 - In the following exercises, solve. 286. At 1:30,...Ch. 2.4 - In the following exercises, solve. 287. Aaron left...Ch. 2.4 - In the following exercises, solve. 288. Marisol...Ch. 2.4 - In the following exercises, solve. 289. Lizette is...Ch. 2.4 - John left his house in Irvine at 8:35 a.m. to...Ch. 2.4 - Sarah wants to arrive at her friend’s wedding at...Ch. 2.4 - Suppose you have six quarters, nine dimes, and...Ch. 2.4 - Do you find it helpful to use a table when solving...Ch. 2.4 - In the table used to solve coin problems, one...Ch. 2.4 - When solving a uniform motion problem, how does...Ch. 2.5 - Graph each inequality on the number line and write...Ch. 2.5 - Graph each inequality on the number line and write...Ch. 2.5 - Graph each inequality on the number line and write...Ch. 2.5 - Graph each inequality on the number line and write...Ch. 2.5 - Solve each inequality, graph the solution on the...Ch. 2.5 - Solve each inequality, graph the solution on the...Ch. 2.5 - Solve each inequality, graph the solution on the...Ch. 2.5 - Solve each inequality, graph the solution on the...Ch. 2.5 - Solve the inequality, graph the solution on the...Ch. 2.5 - Solve the inequality, graph the solution on the...Ch. 2.5 - Solve the inequality 9y+2(y+6)5y24 , graph the...Ch. 2.5 - Solve the inequality 6u+8(u1)10u+32 , graph the...Ch. 2.5 - Solve the inequality 4b3(3b)5(b6)+2b , graph the...Ch. 2.5 - Solve the inequality 9h7(2h)8(h+11)+8h , graph the...Ch. 2.5 - Solve the inequality 14x112x16x+78 , graph the...Ch. 2.5 - Solve the inequality 25z13z115z35 , graph the...Ch. 2.5 - Translate and solve. Then graph the solution on...Ch. 2.5 - Translate and solve. Then graph the solution on...Ch. 2.5 - Angie has $20 to spend on juice boxes for her...Ch. 2.5 - Daniel wants to surprise his girlfriend with a...Ch. 2.5 - Sergio and Lizeth have a very tight vacation...Ch. 2.5 - Rameen’s heating bill is $5.42 per month plus...Ch. 2.5 - Caleb has a pet sitting business. He charges $32...Ch. 2.5 - Elliot has a landscape maintenance business. 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Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
What is a Linear Equation in One Variable?; Author: Don't Memorise;https://www.youtube.com/watch?v=lDOYdBgtnjY;License: Standard YouTube License, CC-BY
Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY