Mathematical Applications for the Management, Life, and Social Sciences
12th Edition
ISBN: 9781337625340
Author: Ronald J. Harshbarger, James J. Reynolds
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Videos
Question
Chapter 3.4, Problem 44E
(a)
To determine
The determinant
(b)
To determine
Whether the matrix has an inverse by using the determinant found in part (a).
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Find the point at which the line (t) = (4, -5,-4)+t(-2, -1,5) intersects the xy plane.
Find the distance from the point (-9, -3, 0) to the line ä(t) = (−4, 1, −1)t + (0, 1, −3) .
1 Find a vector parallel to the line defined by the parametric equations
(x(t)
=
-2t
y(t)
== 1- 9t
z(t)
=
-1-t
Additionally, find a point on the line.
Chapter 3 Solutions
Mathematical Applications for the Management, Life, and Social Sciences
Ch. 3.1 - (a) Do matrices A and B have the same...Ch. 3.1 -
Ch. 3.1 - 3. (a) What matrix D must be added to matrix A...Ch. 3.1 - Prob. 4CPCh. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Prob. 4ECh. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...
Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Prob. 9ECh. 3.1 - Prob. 10ECh. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - In Problems 15-28, perform the operations if...Ch. 3.1 - Prob. 25ECh. 3.1 - In Problems 15-28, perform the operations if...Ch. 3.1 - Prob. 27ECh. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - Prob. 30ECh. 3.1 - In Problems , find and.
Ch. 3.1 - In Problems , find and.
Ch. 3.1 - Prob. 33ECh. 3.1 - 34. Find and if
Ch. 3.1 - 35. Endangered species The tables below give the...Ch. 3.1 - 36. Asian demographics The following tables show...Ch. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - 39. Sales Let matrix A represent the sales (in...Ch. 3.1 - 40. Opinion polls A poll of people revealed...Ch. 3.1 - Prob. 41ECh. 3.1 - 42. National health expenditures The following...Ch. 3.1 - Prob. 43ECh. 3.1 - 44. Debt payment Ace, Baker, and Champ are being...Ch. 3.1 - Prob. 45ECh. 3.1 - Prob. 46ECh. 3.1 - 47. Management Management is attempting to...Ch. 3.1 -
48. Ranking To rank the five members of a...Ch. 3.1 - 49. Production and inventories Operating from two...Ch. 3.1 - Prob. 50ECh. 3.1 - 51. Management In an evaluation of labor...Ch. 3.1 - Prob. 52ECh. 3.1 - 53. For the data in the Problem , use an Excel...Ch. 3.1 - 54. For the data in problem, use an Excel...Ch. 3.2 - What is element if with and
Ch. 3.2 - 2. Find the product.
and
Ch. 3.2 - 3. (a) Compute if and
(b) Can the product...Ch. 3.2 - In Problems 1-4, multiply the matrices.
Ch. 3.2 - In Problems 1-4, multiply the matrices.
Ch. 3.2 - In Problems 1-4, multiply the matrices.
Ch. 3.2 - In Problems 1-4, multiply the matrices.
Ch. 3.2 - In Problems 5-24, use matrices through. In...Ch. 3.2 - In Problems 5-24, use matrices through. In...Ch. 3.2 - In Problems 5-24, use matrices through. In...Ch. 3.2 - Prob. 8ECh. 3.2 - Prob. 9ECh. 3.2 - Prob. 10ECh. 3.2 - Prob. 11ECh. 3.2 - In Problems 5-24, use matrices through. In...Ch. 3.2 - In Problems 5-24, use matrices through. In...Ch. 3.2 - Prob. 14ECh. 3.2 - In Problems 5-24, use matrices through. In...Ch. 3.2 - Prob. 16ECh. 3.2 - Prob. 17ECh. 3.2 - Prob. 18ECh. 3.2 - Prob. 19ECh. 3.2 - Prob. 20ECh. 3.2 - Prob. 21ECh. 3.2 - Prob. 22ECh. 3.2 - In Problems 5-24, use matrices through. In...Ch. 3.2 - Prob. 24ECh. 3.2 - In Problems 25-34, use the matrices below....Ch. 3.2 - Prob. 26ECh. 3.2 - Prob. 27ECh. 3.2 - Prob. 28ECh. 3.2 - Prob. 29ECh. 3.2 - Prob. 30ECh. 3.2 - Prob. 31ECh. 3.2 - Prob. 32ECh. 3.2 - Prob. 33ECh. 3.2 - Prob. 34ECh. 3.2 - Prob. 35ECh. 3.2 - Prob. 36ECh. 3.2 - Prob. 37ECh. 3.2 - 38. For
Are and defined?
What size is each...Ch. 3.2 - Prob. 39ECh. 3.2 - In each of Problems , substitute the given values...Ch. 3.2 - Prob. 41ECh. 3.2 - Prob. 42ECh. 3.2 - Prob. 43ECh. 3.2 - Prob. 44ECh. 3.2 - 45. Car pricing A car dealer can buy midsize cars...Ch. 3.2 - . Revenue A clothing manufacturer has factories...Ch. 3.2 - Prob. 47ECh. 3.2 - . Area and population Matrix below gives the...Ch. 3.2 - 49. Population dynamics Suppose that for a...Ch. 3.2 - 50. Nutrition Suppose the weights (in grams) and...Ch. 3.2 - Prob. 51ECh. 3.2 - Encoding messages Multiplication by a matrix can...Ch. 3.2 - Oil refineries When gasoline is refined from...Ch. 3.2 - 54. Production A manufacturer of small kitchen...Ch. 3.2 - 55. Accounting The annual budget of the Magnum...Ch. 3.2 - 56. Accounting Consider the original budget...Ch. 3.3 - CHECKPOINT
(a) Write the augmented matrix for...Ch. 3.3 - Prob. 2CPCh. 3.3 - CHECKPOINT
For each system of equations, the...Ch. 3.3 - CHECKPOINT
For each system of equations, the...Ch. 3.3 - Prob. 5CPCh. 3.3 - In a problem 1 and 2 use the indicated row...Ch. 3.3 -
In problem 1 and 2, use the indicated row...Ch. 3.3 - In problem 3 and 4, write the augmented matrix...Ch. 3.3 - In problem 3 and 4, write the augmented matrix...Ch. 3.3 -
In problem 5-10, an augmented matrix for a...Ch. 3.3 - Prob. 6ECh. 3.3 - In problem 5-10, an augmented matrix for a system...Ch. 3.3 - In problem 5-10, an augmented matrix for a system...Ch. 3.3 - In problem 5-10, an augmented matrix for a system...Ch. 3.3 - Prob. 10ECh. 3.3 -
In problem 11-16, use row operations on...Ch. 3.3 -
In problem 11-16, use row operations on...Ch. 3.3 - In problem 11-16, use row operations on augmented...Ch. 3.3 -
In problem 11-16, use row operations on augmented...Ch. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.3 -
In problem 17- 20, a system of linear equations...Ch. 3.3 -
In problem 17- 20, a system of linear equations...Ch. 3.3 - In problem 17- 20, a system of linear equations...Ch. 3.3 -
In problem 17- 20, a system of linear equations...Ch. 3.3 - Prob. 21ECh. 3.3 - Prob. 22ECh. 3.3 - Prob. 23ECh. 3.3 - In systems of equations in problem 23 – 36 may...Ch. 3.3 - Prob. 25ECh. 3.3 - Prob. 26ECh. 3.3 - Prob. 27ECh. 3.3 -
In systems of equations in problem 23 – 36 may...Ch. 3.3 - Prob. 29ECh. 3.3 - In systems of equations in problem 23 – 36 may...Ch. 3.3 - Prob. 31ECh. 3.3 - In systems of equations in problem 23 – 36 may...Ch. 3.3 - Prob. 33ECh. 3.3 - Prob. 34ECh. 3.3 - Prob. 35ECh. 3.3 - Prob. 36ECh. 3.3 - Prob. 37ECh. 3.3 - Prob. 38ECh. 3.3 - Prob. 39ECh. 3.3 - Prob. 40ECh. 3.3 - Prob. 41ECh. 3.3 - Prob. 42ECh. 3.3 - Prob. 43ECh. 3.3 - Prob. 44ECh. 3.3 - 45. Nutrition A preschool has Campbell’s Chunky...Ch. 3.3 -
46. Ticket sales A 3500-seat theatre sells...Ch. 3.3 -
47. Investment A man has $235,000 invested in...Ch. 3.3 -
48. Loans A bank lent $1.2 million for the...Ch. 3.3 -
49. Car rental patterns A car rental agency in...Ch. 3.3 -
50. Nutrition A psychologist studying the...Ch. 3.3 - 51. Nutrition The following table gives the...Ch. 3.3 -
52. Investment A brokerage house offers three...Ch. 3.3 -
53. Investment Suppose that portfolios I and II...Ch. 3.3 - 54. Nutrition Each ounce of substance A supplies...Ch. 3.3 - 55. Nutrition A glass of skim milk supplies 0.1 mg...Ch. 3.3 -
56. Transportation The King Trucking Company has...Ch. 3.3 - Nutrition A botanist can purchase plant food of...Ch. 3.3 - Traffic flow In the analyst of traffic flow, a...Ch. 3.3 - Nutrition Three different bacteria are cultured in...Ch. 3.3 - Irrigation An irrigation system allows water to...Ch. 3.3 - Investment An investment club has set a goal to...Ch. 3.3 - A trust account client has to be invested. The...Ch. 3.3 - 63. Investment A brokerage house offers three...Ch. 3.4 - [Type here]
CHECKPOINT
Are the matricesand...Ch. 3.4 - Prob. 2CPCh. 3.4 - Prob. 3CPCh. 3.4 - [Type text]
If is a matrix and is its inverse,...Ch. 3.4 - Prob. 2ECh. 3.4 - Prob. 3ECh. 3.4 - Prob. 4ECh. 3.4 - [Type text]
In Problems 5-10, find the inverse...Ch. 3.4 - [Type text]
In Problems 5-10, find the inverse...Ch. 3.4 - Prob. 7ECh. 3.4 - Prob. 8ECh. 3.4 - Prob. 9ECh. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - Prob. 13ECh. 3.4 - Prob. 14ECh. 3.4 - [Type here]
In Problems 15-20, find the inverse...Ch. 3.4 - Prob. 16ECh. 3.4 - Prob. 17ECh. 3.4 - [Type here]
In Problems 15-20, find the inverse...Ch. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Prob. 21ECh. 3.4 - Prob. 22ECh. 3.4 - [Type here]
In Problems 23-26, the inverse of...Ch. 3.4 - [Type here]
In Problems 23-26, the inverse of...Ch. 3.4 - [Type here]
In Problems 23-26, the inverse of...Ch. 3.4 - [Type here]
In Problems 23-26, the inverse of...Ch. 3.4 - Prob. 27ECh. 3.4 - [Type here]
28. Use the inverse found in Problem...Ch. 3.4 - Prob. 29ECh. 3.4 - Prob. 30ECh. 3.4 - [Type here]
In Problems 29-32, use inverse...Ch. 3.4 - [Type here]
In Problems 29-32, use inverse...Ch. 3.4 - Prob. 33ECh. 3.4 - Prob. 34ECh. 3.4 - Prob. 35ECh. 3.4 - Prob. 36ECh. 3.4 - Prob. 37ECh. 3.4 - Prob. 38ECh. 3.4 - Prob. 39ECh. 3.4 - Prob. 40ECh. 3.4 - Prob. 41ECh. 3.4 - Prob. 42ECh. 3.4 - Prob. 43ECh. 3.4 - Prob. 44ECh. 3.4 - Prob. 45ECh. 3.4 - Prob. 46ECh. 3.4 - Prob. 47ECh. 3.4 - Prob. 48ECh. 3.4 - Prob. 49ECh. 3.4 - Prob. 50ECh. 3.4 - 51. Competition A product is made by only two...Ch. 3.4 -
52. Demographics Suppose that a government study...Ch. 3.4 -
In Problems 53-63, set up each system of...Ch. 3.4 -
In Problems 53-63, set up each system of...Ch. 3.4 -
In Problems, set up each system of equations and...Ch. 3.4 -
In problems , set up each system of equations...Ch. 3.4 - In Problems 5363, set up each system of equations...Ch. 3.4 - In Problems 5363, set up each system of equations...Ch. 3.4 - In Problems set up each system of equations and...Ch. 3.4 - In Problems set up each system of equations and...Ch. 3.4 - In Problems 53-63, set up each system of equations...Ch. 3.4 - In Problems set up each system of equations and...Ch. 3.5 - CHECKPOINT
The following technology matrix for a...Ch. 3.5 - Prob. 2CPCh. 3.5 - CHECKPOINT
3. Suppose a primitive economy has wood...Ch. 3.5 - Prob. 4CPCh. 3.5 - The following technology matrix for a simple...Ch. 3.5 - For the economy in Problem 1, what industry is...Ch. 3.5 - Prob. 3ECh. 3.5 - Prob. 4ECh. 3.5 - The following technology matrix describes the...Ch. 3.5 - The following technology matrix describes the...Ch. 3.5 - Prob. 7ECh. 3.5 - Prob. 8ECh. 3.5 - Prob. 9ECh. 3.5 - Prob. 10ECh. 3.5 - Suppose a primitive economy consists of two...Ch. 3.5 - Suppose an economy has two industries, agriculture...Ch. 3.5 - Prob. 13ECh. 3.5 - Prob. 14ECh. 3.5 - Suppose the economy of an underdeveloped country...Ch. 3.5 - Suppose a simple economy with only an agricultural...Ch. 3.5 - Prob. 17ECh. 3.5 - An underdeveloped country has an agricultural...Ch. 3.5 - A simple economy has an electronic components...Ch. 3.5 - Prob. 20ECh. 3.5 - A primitive economy consists of a fishing industry...Ch. 3.5 - An economy has a manufacturing industry and a...Ch. 3.5 - Prob. 23ECh. 3.5 - Prob. 24ECh. 3.5 - Prob. 25ECh. 3.5 - Interdepartmental costs Within a company is a...Ch. 3.5 - Suppose that an economy has three industries...Ch. 3.5 - Prob. 28ECh. 3.5 - Suppose that the economy of a small nation has an...Ch. 3.5 - Suppose an economy has the same technology matrix...Ch. 3.5 - Suppose that a simple economy has three...Ch. 3.5 - Prob. 32ECh. 3.5 - Problems 33-38 refer to closed Leontief models....Ch. 3.5 - Problems 33-38 refer to closed Leontief models....Ch. 3.5 - Problems 33-38 refer to closed Leontief models....Ch. 3.5 - Problems 33-38 refer to closed Leontief models....Ch. 3.5 - Problems 33-38 refer to closed Leontief models....Ch. 3.5 - Problems 33-38 refer to closed Leontief models.
A...Ch. 3.5 - Prob. 39ECh. 3.5 - Card tables are made by joining legs and a top...Ch. 3.5 - Prob. 41ECh. 3.5 - A log carrier has a body made from a -ft length of...Ch. 3 - Use the matrices below a needed to complete...Ch. 3 - Use the matrices below a needed to complete...Ch. 3 - Prob. 3RECh. 3 - Prob. 4RECh. 3 - Prob. 5RECh. 3 - Prob. 6RECh. 3 - Prob. 7RECh. 3 - Prob. 8RECh. 3 - Prob. 9RECh. 3 - Prob. 10RECh. 3 - Prob. 11RECh. 3 - Prob. 12RECh. 3 - Prob. 13RECh. 3 - Prob. 14RECh. 3 - Prob. 15RECh. 3 - Prob. 16RECh. 3 - Prob. 17RECh. 3 - Prob. 18RECh. 3 - Prob. 19RECh. 3 - Prob. 20RECh. 3 - Prob. 21RECh. 3 - Prob. 22RECh. 3 - Prob. 23RECh. 3 - Prob. 24RECh. 3 - Prob. 25RECh. 3 - Prob. 26RECh. 3 - Prob. 27RECh. 3 - Prob. 28RECh. 3 - Prob. 29RECh. 3 - Prob. 30RECh. 3 - In Problems 30-36, solve each system using...Ch. 3 - Prob. 32RECh. 3 - In Problems 30-36, solve each system using...Ch. 3 - Prob. 34RECh. 3 - Prob. 35RECh. 3 - Prob. 36RECh. 3 - Prob. 37RECh. 3 - Prob. 38RECh. 3 - Prob. 39RECh. 3 - Prob. 40RECh. 3 - Prob. 41RECh. 3 - Prob. 42RECh. 3 - Prob. 43RECh. 3 - Prob. 44RECh. 3 - Prob. 45RECh. 3 - Prob. 46RECh. 3 - Prob. 47RECh. 3 - Prob. 48RECh. 3 - The Burr Cabinet Company manufactures bookcases...Ch. 3 - Prob. 50RECh. 3 - A small church choir is made up of men and women...Ch. 3 - Manufacturing Two departments of a firm, and ,...Ch. 3 - Prob. 53RECh. 3 - Investment A woman has to invest. She has decided...Ch. 3 - Nutrition A biologist is growing three different...Ch. 3 - Transportation An airline company has three types...Ch. 3 - Economy models An economy has a shipping industry...Ch. 3 - Economy models A simple economy has a shoe...Ch. 3 - Economy models A look at the industrial sector of...Ch. 3 - Economy models Suppose a closed Leontief model for...Ch. 3 - Prob. 1TCh. 3 - Prob. 2TCh. 3 - Prob. 3TCh. 3 - Prob. 4TCh. 3 - Prob. 5TCh. 3 - Prob. 6TCh. 3 - Prob. 7TCh. 3 - Prob. 8TCh. 3 - Prob. 9TCh. 3 - Prob. 10TCh. 3 - Prob. 11TCh. 3 - Prob. 12TCh. 3 - Prob. 13TCh. 3 - Prob. 14TCh. 3 - Suppose that the solution of an investment problem...Ch. 3 - Prob. 16TCh. 3 - Prob. 17TCh. 3 - Prob. 18TCh. 3 - Prob. 19TCh. 3 - Prob. 20TCh. 3 -
21. Suppose the technology matrix for a closed...Ch. 3 -
Use the following information in Problem ...Ch. 3 -
Use the following information in Problem ...Ch. 3 - Prob. 24TCh. 3 - Prob. 1EAGP1Ch. 3 - Prob. 2EAGP1Ch. 3 - Prob. 3EAGP1Ch. 3 - Prob. 4EAGP1Ch. 3 - Prob. 5EAGP1Ch. 3 - Prob. 6EAGP1Ch. 3 - Prob. 7EAGP1Ch. 3 - Prob. 1EAGP2Ch. 3 - Prob. 2EAGP2Ch. 3 - Prob. 3EAGP2Ch. 3 - Prob. 4EAGP2
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
- Find the (perpendicular) distance from the line given by the parametric equations (x(t) = 5+9t y(t) = 7t = 2-9t z(t) to the point (-1, 1, −3).arrow_forwardLet ä(t) = (3,-2,-5)t + (7,−1, 2) and (u) = (5,0, 3)u + (−3,−9,3). Find the acute angle (in degrees) between the lines:arrow_forwardNo chatgpt pls will upvotearrow_forward
- A tank initially contains 50 gal of pure water. Brine containing 3 lb of salt per gallon enters the tank at 2 gal/min, and the (perfectly mixed) solution leaves the tank at 3 gal/min. Thus, the tank is empty after exactly 50 min. (a) Find the amount of salt in the tank after t minutes. (b) What is the maximum amount of salt ever in the tank?arrow_forwardDraw a picture of a normal distribution with mean 70 and standard deviation 5.arrow_forwardWhat do you guess are the standard deviations of the two distributions in the previous example problem?arrow_forward
- 1 What is the area of triangle ABC? 12 60° 60° A D B A 6√√3 square units B 18√3 square units 36√3 square units D 72√3 square unitsarrow_forwardEach answer must be justified and all your work should appear. You will be marked on the quality of your explanations. You can discuss the problems with classmates, but you should write your solutions sepa- rately (meaning that you cannot copy the same solution from a joint blackboard, for exam- ple). Your work should be submitted on Moodle, before February 7 at 5 pm. 1. True or false: (a) if E is a subspace of V, then dim(E) + dim(E) = dim(V) (b) Let {i, n} be a basis of the vector space V, where v₁,..., Un are all eigen- vectors for both the matrix A and the matrix B. Then, any eigenvector of A is an eigenvector of B. Justify. 2. Apply Gram-Schmidt orthogonalization to the system of vectors {(1,2,-2), (1, −1, 4), (2, 1, 1)}. 3. Suppose P is the orthogonal projection onto a subspace E, and Q is the orthogonal projection onto the orthogonal complement E. (a) The combinations of projections P+Q and PQ correspond to well-known oper- ators. What are they? Justify your answer. (b) Show…arrow_forwardpleasd dont use chat gptarrow_forward
- 1. True or false: (a) if E is a subspace of V, then dim(E) + dim(E+) = dim(V) (b) Let {i, n} be a basis of the vector space V, where vi,..., are all eigen- vectors for both the matrix A and the matrix B. Then, any eigenvector of A is an eigenvector of B. Justify. 2. Apply Gram-Schmidt orthogonalization to the system of vectors {(1, 2, -2), (1, −1, 4), (2, 1, 1)}. 3. Suppose P is the orthogonal projection onto a subspace E, and Q is the orthogonal projection onto the orthogonal complement E. (a) The combinations of projections P+Q and PQ correspond to well-known oper- ators. What are they? Justify your answer. (b) Show that P - Q is its own inverse. 4. Show that the Frobenius product on n x n-matrices, (A, B) = = Tr(B*A), is an inner product, where B* denotes the Hermitian adjoint of B. 5. Show that if A and B are two n x n-matrices for which {1,..., n} is a basis of eigen- vectors (for both A and B), then AB = BA. Remark: It is also true that if AB = BA, then there exists a common…arrow_forwardQuestion 1. Let f: XY and g: Y Z be two functions. Prove that (1) if go f is injective, then f is injective; (2) if go f is surjective, then g is surjective. Question 2. Prove or disprove: (1) The set X = {k € Z} is countable. (2) The set X = {k EZ,nЄN} is countable. (3) The set X = R\Q = {x ER2 countable. Q} (the set of all irrational numbers) is (4) The set X = {p.√2pQ} is countable. (5) The interval X = [0,1] is countable. Question 3. Let X = {f|f: N→ N}, the set of all functions from N to N. Prove that X is uncountable. Extra practice (not to be submitted). Question. Prove the following by induction. (1) For any nЄN, 1+3+5++2n-1 n². (2) For any nЄ N, 1+2+3++ n = n(n+1). Question. Write explicitly a function f: Nx N N which is bijective.arrow_forward3. Suppose P is the orthogonal projection onto a subspace E, and Q is the orthogonal projection onto the orthogonal complement E. (a) The combinations of projections P+Q and PQ correspond to well-known oper- ators. What are they? Justify your answer. (b) Show that P - Q is its own inverse.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
Algebra for College Students
Algebra
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
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