College Algebra 1st Edition
ISBN: 9781938168383
Author: Jay Abramson
Publisher: Jay Abramson
1 Prerequisites 2 Equations And Inequalities 3 Functions 4 Linear Functions 5 Polynomial And Rational Functions 6 Exponential And Logarithmic Functions 7 Systems Of Equations And Inequalities 8 Analytic Geometry 9 Sequences, Probability And Counting Theory Chapter7: Systems Of Equations And Inequalities
7.1 Systems Of Linear Equations: Two Variables 7.2 Systems Of Linear Equations: Three Variables 7.3 Systems Of Nonlinear Equations And Inequalities: Two Variables 7.4 Partial Fractions 7.5 Matrices And Matrix Operations 7.6 Solving Systems With Gaussian Elimination 7.7 Solving Systems With Inverses 7.8 Solving Systems With Cramer's Rule Chapter Questions Section7.2: Systems Of Linear Equations: Three Variables
Problem 1TI: Solve the system of equations in three variables. 2x+y2z=13x3yz=5x2y+3z=6 Problem 2TI: Solve the system of equations in three variables. x+y+z=2y3z=12x+y+5z=0 Problem 3TI: Solve the following system x+y+z=73x2yz=4x+6y+5z=24 Problem 1SE: Can a linear system of three equations have exactly two solutions? Explain why or why not Problem 2SE: If a given ordered triple solves the system of equations, is that solution unique? If so, explain... Problem 3SE: If a given ordered triple does not solve the system of equations, is there no solution? If so,... Problem 4SE: Using the method of addition, is there only one way to solve the system? Problem 5SE: Can you explain whether there can be only one method to solve a linear system of equations? If yes,... Problem 6SE: For the Following exercises, determine whether the ordered triple given is the solution to the... Problem 7SE: For the Following exercises, determine whether the ordered triple given is the solution to the... Problem 8SE: For the Following exercises, determine whether the ordered triple given is the solution to the... Problem 9SE: For the Following exercises, determine whether the ordered triple given is the solution to the... Problem 10SE: For the Following exercises, determine whether the ordered triple given is the solution to the... Problem 11SE: For the following exercises, solve each system by substitution. 3x4y+2z=152x+4y+z=162x+3y+5z=20 Problem 12SE: For the following exercises, solve each system by substitution. 5x2y+3z=202x4y3z=9x+6y8z=21 Problem 13SE: For the following exercises, solve each system by substitution. 5x+2y+4z=93x+2y+z=104x3y+5z=3 Problem 14SE: For the following exercises, solve each system by substitution. 4x3y+5z=31x+2y+4z=20x+5y2z=29 Problem 15SE: For the following exercises, solve each system by substitution. 15. 5x2y+3z=44x+6y7z=13x+2yz=4 Problem 16SE: For the following exercises, solve each system by substitution. 16. 4x+6y+9z=05x+2y6z=37x4y+3z=3 Problem 17SE: For the following exercises, solve each system by substitution. 17. 2xy+3z=175x+4y2z=462y+5z=7 Problem 18SE: For the following exercises, solve each system by substitution. 5x6y+3z=50x+4y=102xz=10 Problem 19SE: For the following exercises, solve each system by Gaussian elimination.... Problem 20SE: For the following exercises, solve each system by Gaussian elimination. 4x+6y2z=86x+9y3z=122x3y+z=4 Problem 21SE: For the following exercises, solve each system by Gaussian elimination. 21.... Problem 22SE: For the following exercises, solve each system by Gaussian elimination.... Problem 23SE: For the following exercises, solve each system by Gaussian elimination. 23.... Problem 24SE: For the following exercises, solve each system by Gaussian elimination. 5x3y+4z=14x+2y3z=0x+5y+7z=11 Problem 25SE: For the following exercises, solve each system by Gaussian elimination. x+y+z=02xy+3z=0xz=0 Problem 26SE: For the following exercises, solve each system by Gaussian elimination.... Problem 27SE: For the following exercises, solve each system by Gaussian elimination. x+y+z=02xy+3z=0xz=1 Problem 28SE: For the following exercises, solve each system by Gaussian elimination. 3x12yz=124x+z=3x+32y=52 Problem 29SE: For the following exercises, solve each system by Gaussian elimination.... Problem 30SE: For the following exercises, solve each system by Gaussian elimination.... Problem 31SE: For the following exercises, solve each system by Gaussian elimination.... Problem 32SE: For the following exercises, solve each system by Gaussian elimination.... Problem 33SE: For the following exercises, solve each system by Gaussian elimination.... Problem 34SE: For the following exercises, solve each system by Gaussian elimination.... Problem 35SE: For the following exercises, solve each system by Gaussian elimination.... Problem 36SE: For the following exercises, solve each system by Gaussian elimination.... Problem 37SE: For the following exercises, solve each system by Gaussian elimination.... Problem 38SE: For the following exercises, solve each system by Gaussian elimination.... Problem 39SE: For the following exercises, solve each system by Gaussian elimination.... Problem 40SE: For the following exercises, solve each system by Gaussian elimination.... Problem 41SE: For the following exercises, solve each system by Gaussian elimination.... Problem 42SE: For the following exercises, solve each system by Gaussian elimination.... Problem 43SE: For the following exercises, solve each system by Gaussian elimination. 43.... Problem 44SE: For the following exercises, solve each system by Gaussian elimination. 44.... Problem 45SE: For the following exercises, solve each system by Gaussian elimination. 45.... Problem 46SE: For the following exercises, solve the system for x, y, and z. 46.... Problem 47SE: For the following exercises, solve the system for x, y, and z. 47. 5x3yz+12=126x+y92+2z=3x+824y+z=4 Problem 48SE: For the following exercises, solve the system for x, y, and z. 48.... Problem 49SE: For the following exercises, solve the system for x, y, and z. 49.... Problem 50SE: For the following exercises, solve the system for x, y, and z. 50.... Problem 51SE: Three even numbers sum up to 108. The smaller is half the larger and the middle number is 34 the... Problem 52SE: Three numbers sum up to 147. The smallest number is half the middle number, which is half the... Problem 53SE: At a family reunion, there were only blood relatives, consisting of children, parents, and... Problem 54SE: An animal shelter has a total of 350 animals comprised of cats, dogs, and rabbits. If the number of... Problem 55SE: Your roommate, Sarah, offered to buy groceries for you and your other roommate. The total bill was... Problem 56SE: Your roommate, John, offered to buy household supplies for you and your other roommate. You live... Problem 57SE: Three coworkers work for the same employer. Their jobs are warehouse manager, office manager, and... Problem 58SE: At a carnival, $2,914.25 in receipts were taken at the end of the day. The cost of a child's ticket... Problem 59SE: A local band sells out for their concert. They sell all 1,175 tickets for a total purse of... Problem 60SE: In a bag, a child has 325 coins worth $19.50. There were three types of coins: pennies, nickels, and... Problem 61SE: Last year, at Haven's Pond Car Dealership, for a particular model of BMW, Jeep, and Toyota, one... Problem 62SE: A recent college graduate took advantage of his business education and invested in three investments... Problem 63SE: You inherit one million dollars. You invest it all in three accounts for one year. The first account... Problem 64SE: You inherit one hundred thousand dollars. You invest it all in three accounts for one year. The... Problem 65SE: The top three countries in oil consumption in a certain year are as follows: the United States,... Problem 66SE: The top three countries in oil production in the same year are Saudi Arabia, the United States, and... Problem 67SE: The top three sources of oil imports for the United States in the same year were Saudi Arabia,... Problem 68SE: The top three oil producers in the United States in a certain year are the Gulf of Mexico, Texas,... Problem 69SE: At one time, in the United States, 398 species of animals were on the endangered species list. The... Problem 70SE: Meat consumption in the United States can be broken into three categories: red meat, poultry, and... Problem 1SE: Can a linear system of three equations have exactly two solutions? Explain why or why not
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Do not perform any calculations, but explain the solution from properties in a linear algebra course.
Transcribed Image Text: 5. The linear system AX = b₁ and Ax = b2 are consistent. Is the system Ax
consistent? Explain your answer.
=
b₁ + b₂ necessarily
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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Step 2: Put x = x1 +x2 in Ax = b1 + b2
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