For each of the systems of equations that follow, use Gaussian elimination to obtain an equivalent...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
For each of the systems of equations that follow, use Gaussian elimination to obtain an equivalent system whose coefficient matrix is in row echelon form. Indicate whether the system is consistent. If the system is consistent and involves no free variables, use back substitution to find the unique solution. If the system is consistent and there are free variables, transform it to reduced row echelon form and find all solutions. (b) (a) x₁-2x₂ = 3 2x₁ - x₂ = 9 (c) x₁ + x₂=0 2x+3x₂=0 3x1 - 2x₂ = 0 2x₁-3x₂ = 5 -4x₁ + 6x₂ = 8 (d) 3x + 2x2-x=4 (e) 2x₁ + 3x2 + x₁ = 1 X₁ + x₂ + x3 = 3 3x₁ +4x₂+2x3 = 4 (1) ₁-3₂ + 2x₁ = 4 2x₁ + 3x₂ - xy = 1 7x1 + 3x₂ + 4xy = 7 41-2x₂+2x3= 1 11x₁ + 2x₂ + x3= 14 (g) x₁ + x₂+x₂+x=0 2x₁ + 3x₂-x3-x4=2 3x1 + 2x2 + x3+x=5 3x₁ + 6x₂-x3-Jq=4 -X₁ + 2x₂x3 = 2 - -2x₁ +21₂ + x = 4 3x + 2x2 + 2xy = 5 -3x₁ + 8x₂ + 5x3 = 17 (j)) + 2x₂-3x3+Xq=1 x2 + 4x3 = 6 -2x1-4x2+7x1-x=1 (1) - (k) x₁ + 3x2 + x3 + x4=3 2x12x2 + x3 + 2x=8 - 5x2 + *4= 5 XI 3x₂ + 2x1 + x₂ - x3 = 1 3 = 2 1+ 4x2 - 2x3 = I 5x₁8x2 + 2x3 = 5 1 (h) x1 = 2x₂ = 3 2x₁ + x₂ = 1 -5r+8b = 4 For each of the systems of equations that follow, use Gaussian elimination to obtain an equivalent system whose coefficient matrix is in row echelon form. Indicate whether the system is consistent. If the system is consistent and involves no free variables, use back substitution to find the unique solution. If the system is consistent and there are free variables, transform it to reduced row echelon form and find all solutions. (b) (a) x₁-2x₂ = 3 2x₁ - x₂ = 9 (c) x₁ + x₂=0 2x+3x₂=0 3x1 - 2x₂ = 0 2x₁-3x₂ = 5 -4x₁ + 6x₂ = 8 (d) 3x + 2x2-x=4 (e) 2x₁ + 3x2 + x₁ = 1 X₁ + x₂ + x3 = 3 3x₁ +4x₂+2x3 = 4 (1) ₁-3₂ + 2x₁ = 4 2x₁ + 3x₂ - xy = 1 7x1 + 3x₂ + 4xy = 7 41-2x₂+2x3= 1 11x₁ + 2x₂ + x3= 14 (g) x₁ + x₂+x₂+x=0 2x₁ + 3x₂-x3-x4=2 3x1 + 2x2 + x3+x=5 3x₁ + 6x₂-x3-Jq=4 -X₁ + 2x₂x3 = 2 - -2x₁ +21₂ + x = 4 3x + 2x2 + 2xy = 5 -3x₁ + 8x₂ + 5x3 = 17 (j)) + 2x₂-3x3+Xq=1 x2 + 4x3 = 6 -2x1-4x2+7x1-x=1 (1) - (k) x₁ + 3x2 + x3 + x4=3 2x12x2 + x3 + 2x=8 - 5x2 + *4= 5 XI 3x₂ + 2x1 + x₂ - x3 = 1 3 = 2 1+ 4x2 - 2x3 = I 5x₁8x2 + 2x3 = 5 1 (h) x1 = 2x₂ = 3 2x₁ + x₂ = 1 -5r+8b = 4
Expert Answer:
Answer rating: 100% (QA)
To solve each system of equations using Gaussian elimination and determine whether the system is con... View the full answer
Related Book For
Smith and Roberson Business Law
ISBN: 978-0538473637
15th Edition
Authors: Richard A. Mann, Barry S. Roberts
Posted Date:
Students also viewed these international, global, thematic questions
-
Within the thematic framework of human rights advocacy, what strategies can be adopted to combat systemic discrimination and promote inclusivity in culturally diverse societies worldwide?
-
Identify the process evaluation article that you chose and explain why you selected this example. Describe the purpose of the evaluation, the informants, the questions asked, and the results of the...
-
What is the effect of cultural commoditization and transformation on local traditions and customs? Give an example. Check Chapter 4 in the textbook for information on cultural commoditization and...
-
Rachael Ray Corporation had the following transactions. 1. Sold land (cost $12,000) for $15,000. 2. Issued common stock for $20,000. 3. Recorded depreciation of $17,000. 4. Paid salaries of $9,000....
-
ABC pharmaceutical corp. is planning on undertaking a new project, the initial cash outlay is $50,000 with projected cash inflows of $20,000 per year for the projects 4-year life, assuming a cost of...
-
a. It is now January 1. You plan to make five deposits of $100 each, one every 6 months, with the first payment being made today. If the bank pays a nominal interest rate of 8% but uses semiannual...
-
What is the probability of drawing 4 tiles in the pattern vowel-consonant-vowel-consonant, in order? You are about to draw Scrabble tiles from a bag without replacement; the bag contains the letters...
-
The bookstore at State University purchases from a vendor sweatshirts emblazoned with the school name and logo. The vendor sells the sweatshirts to the store for $38 apiece. The cost to the bookstore...
-
Find the area enclosed by the closed curve obtained by joining the ends of the spiral T = 10, 0 <0 < 5.8 by a straight line segment.
-
The Dapper-Dons Partnership was formed ten years ago as a general partnership to custom tailor men's clothing. Dapper-Dons is located at 123 Flamingo Drive in City, ST, 54321. Bob Dapper manages the...
-
Use the figure for Questions 11 and 12. 11. If ALMN is isosceles and T is the midpoint of LN, which postulate or theorem can be used to prove AMLT = AMNT? A AAA B AAS C SSS 12. If AMLTAMNT, what is...
-
Riki Co. acquires the entire share capital of Doom Co. by issuing 100,000 new P1 ordinary shares at a fair value at the acquisition date of P2.50. The professional fees associated with the...
-
use this noisy image then Write a code to keep only image edges Write a code to remove the noise from the image Write a code to keep only edges of the result from b) use java as a programing language...
-
What factors that have led to increased health care costs? what necessary skills that you would hope to possess in the potential role as a finance manager when making capital purchases and how this...
-
Make a Java class to find the difference between the sum of the cubes of the first one hundred natural numbers (1 to 100) and the cube of the sum of the first 100 natural numbers. You may use either...
-
Discuss what four steps should be implemented when developing a financial plan
-
1. Describe the functions that a package can perform. Which function is most important? Why? 2. When developing a package, what are the major issues that a marketer should consider? 3. In what ways...
-
Write a declaration for each of the following: a. A line that extends from point (60, 100) to point (30, 90) b. A rectangle that is 20 pixels wide, 100 pixels high, and has its upper-left corner at...
-
Robert V. Gross owned certain land on which he proposed to construct an eighty-three-unit apartment house. The land, however, was subject to a restriction imposed by a 1970 deed to a predecessor in...
-
On this * * * appeal, Pacific Custom Pools, Inc., challenges the trial courts granting of summary judgment based on the failure of Pacific Custom Pools to substantially comply with the contractors...
-
Civil Code 1719, subdivision (a) provides in part that any person who draws a check that is dishonored due to insufficient funds shall be liable to the payee for the amount owing upon the check and...
-
What role does growth-need strength play in the job characteristics model?
-
Explain the difference between halo errors and recency errors in performance appraisal.
-
When is a team effective?
Study smarter with the SolutionInn App