Solve the following system of linear equations: −p + q + 2r = 8 (1) p...

Solve the following system of linear equations:

−p + q + 2r = 8 (1)

p + q + 2r = 0 (2)

2q − 2r = 2 (3).

The sum of the values of p, q and r of the solution is

Solutions

Expert Solution

The solution uses the basic knowledge of solving a non homogeneous system of equations, how to find rank of a matrix, what is an augmented matrix, How to apply row operations to reduce any matrix to an upper triangular matrix.
back substitution means starting from last equation and finding the variable's value then using that variable's value in 2nd equation and then solving the first equation for the first variable.

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

Question No.1: Solve the following system of two linear equations with two variables x and y...

Question No.1: Solve the following system of two linear equations with two variables x and y by “Equating the equations” method. ? = ?? − ?? ??? ? = −? + 5 Question No.2: Is this matrix ? = [ ? ? ? ? ] singular or non-singular? Question No. 3: Solve the following operations with the help of “PEMDAS”. ? ? − (?? ÷ ?) × ? ÷ ? − ? × ? + ?? ÷ ?3 Question No.4:...

Question 1 Using MATLAB solve the following system of linear simultaneous equations 3x + 2y -...

Question 1 Using MATLAB solve the following system of linear simultaneous equations 3x + 2y - z = 10........... [1] -x + 3y + 2z = 5........... [2] x - y - z = -1 .................[3] s + 2t - 3u + 4v = 12........... [1] 2s + 2t - 2u + 3v = 10......... [2] t + u = -1............................ [3] s - t + u - 2v = -4................ [4]

1. Given the following system equations of price (P) and quantity (Q) determination in a widget...

1. Given the following system equations of price (P) and quantity (Q) determination in a widget market: SHOW ALL WORK! Demand: Q = 100 - 4P + 2G …..(1) Supply: Q= 60 + 10P – 3N ……(2) Where the price of substitute good, G = 10, and the cost of production N = 8. 1-a) by using the repeated substitution method only, please find equilibrium P and Q. 1-b) if G is up by 2, shows the impact of...

Given the following supply and demand equations, solve the following supply: p=q Demand: p=200-p a) What...

Given the following supply and demand equations, solve the following supply: p=q Demand: p=200-p a) What is the market equilibrium price and quantity? b) What is the Consumer surplus and the producer surplus? c) The government enacts a price ceiling of $120. What is the new consumer surplus? d) Assume now the government enacts a price ceiling of $20. What is the new consumer surplus? e) When the price ceiling is $20, consumer surplus declines, compared to the market equilibrium....

1) Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no...

1) Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answer in terms of the parameters t and/or s.) 3y + 2z = 1 2x − y − 3z = 4 2x + 2y − z = 5 (x, y, z) = 2) Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no solution, enter NO SOLUTION....

SET UP BUT DO NOT SOLVE the following system of linear equations: A company sells three...

SET UP BUT DO NOT SOLVE the following system of linear equations: A company sells three sizes of fruit trays. The small size contains 200 gr of watermelons and 100 gr of grapes. The medium size contains 400 gr of watermelons, 100 gr of pineapples, and 300 gr of grapes. The large size contains 600 gr of watermelons, 200 gr of pineapples, and 400 gr of grapes. Suppose that the company receives an order for 28 kg of watermelons, 6...

Solve the linear system of equations Ax = b, and give the rank of the matrix...

Solve the linear system of equations Ax = b, and give the rank of the matrix A, where A = 1 1 1 -1 0 1 0 2 1 0 1 1 b = 1 2 3

Use a software program or a graphing utility to solve the system of linear equations. (If...

Use a software program or a graphing utility to solve the system of linear equations. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set x5 = t and solve for x1, x2, x3, and x4 in terms of t.) x1 − x2 + 2x3 + 2x4 + 6x5 = 16 3x1 − 2x2 + 4x3 + 4x4 + 12x5 = 33 x2 − x3 − x4 − 3x5 = −9 2x1...

Use a software program or a graphing utility to solve the system of linear equations. (If...

The following matrix is the augmented matrix for a system of linear equations. A = 1...

The following matrix is the augmented matrix for a system of linear equations. A = 1 1 0 1 1 0 0 1 3 3 0 0 0 1 1 2 2 0 5 5 (a) Write down the linear system of equations whose augmented matrix is A. (b) Find the reduced echelon form of A. (c) In the reduced echelon form of A, mark the pivot positions. (d) Does the system have no solutions, exactly one solution or infinitely...

Subjects