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....
-
In Florida sunscreen and sunglasses are vital items If the tax on sellers of these items is doubled from 5.5 percent to 11 percent who will pay most of the tax increase the buyer or the seller. Will...
-
What mechanism is used to provide a systematic assessment of an organization's performance in implementing socially responsible programs, often based on predefined goals?
-
True or False. Gathering data is all that is required for a successful trending program.
-
Paseo Industries has adopted the following production budget for the first 4 months of 2013. Each unit requires 3 pounds of raw materials costing $2 per pound. On December 31, 2012, the ending raw...
-
you are working at the law firm of Hamer, Huerta, Jordan, and Yousafzai. The client, Hilda, stopped by to sign a few business documents that you recently prepared. Suddenly, she reveals to you and a...
-
We became a debtor nation in ________. a) 1975 c) 1985 b) 1980 d) 1990
-
Perfect price discrimination eliminates __________ of the customers consumer surplus. a) all b) most c) some d) none
-
Algeria has a negative trade balance of $7 billion. If it has a positive balance of goods of $10 billion, how much is its balance of services?
-
During the 1980s and 1990s, ______. a) both American investment abroad and foreign investment in the United States increased b) both American investment abroad and foreign investment in the United...
-
Which statement is true? a) When you decide which doctor to go to, your only concern is the quality of the medical service you will receive. b) People differentiate among goods and services based not...
-
Assume that you would start a business of having a hot dog truck at the KPU Surrey campus. a. Identify and list your fixed costs and then identify your monthly fixed cost to run a hot dog stand....
-
The 2017 financial statements of the U.S. government are available at: https://www.fiscal.treasury.gov/fsreports/rpt/finrep/fr/fr_index.htm Use these to answer the following questions: a. Statement...
-
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...
-
Explain the building blocks of accounting: ethics, principles, and assumptions.
-
On May 1, 2025, Park Flying School Ltd., a company that provides flying lessons, was started with an investment of 45,000 cash in the business. Following are the assets and liabilities of the company...
-
The historical cost basis results in: a. initially recording assets at cost and adjusting when the current value changes. b. keeping activities of an entity separate and distinct from its owner. c....
Study smarter with the SolutionInn App