Let's Get RealA scientist uses technology to solve a nonhomogeneous system of thirty-three linearequations in three hundred eighty-eight unknowns and finds that three hundred fifty-eight of the unknowns are free variables. It is very common in science that we can reusethe same equations when a situation changes but with the slight modification that theright side of each equation changes.a. Can the scientist be certain that, if the right sides of the equations are changed,the new nonhomogeneous system will have a solution?O YesNob. Defend your response.

A scientist uses technology to solve a nonhomogeneous system of thirty-three linear equations in…

Answered: A scientist uses technology to solve a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Problem 3. Determine whether the given linear equations are in standard form (a₁ ·x₁ + a₂ ·x₂ + az ·x₂ +...+ a₂ ·x₂ = b) and for each equation find the number of variables (n), the coefficients a₁, 92, ... an and the constant term b. a) 5x₁+3x2-6x3+X4+8X5=7 b) -3x₁+4x2-X3=-2 c) X₁+2x3-5x2+3x4-6X5+X6=0 d) 6x₁+5X4+3x2+7x3=10
A special diet needs to include exactly 340 units of calcium, 180 units of iron, and 220 units of vitamin A. the number of units per ounce of each ingredient for each of the foods is indicated in the table. units per ounce food A food B food C calcium 30 10 20 iron 10 10 20 vitamin A 10 30 20 A) how many ounces of each food must be used to meet the diet requirements? set up a 3x3 system of linear equations and solve it by Gauss-Jordan Elimination. B) how is the diet in part (A) affected if the vitamin A requirement is dropped?
If two systems of linear equations have different numbers of equations, then the two systems are not equivalent. True False
According to projections through the year 2030, the population y of the given state in year x is approximated by State A: - 4x + y = 11,400 State B: 141x + y = 7,000 where x = 0 corresponds to the year 2000 and y is in thousands. In what year do the two states have the same population? The two states will have the same population in the year
Solve the following system of linear equations: 5x1+10x2-10x3 = -75 -X1+8x3 = 29 -x1-3x₂= 12 If the system has no solution, demonstrate this by giving a row-echelon form of the augmented matrix for the system. If the system has infinitely many solutions, select "The system has at least one solution". Your answer may use expressions involving the parameters r, s, and t. You can resize a matrix (when appropriate) by clicking and dragging the bottom-right corner of the matrix. The system has no solutions 0 0 0 Row-echelon form of augmented matrix: 0 00 000
Solve the following system of linear equations: How many solutions are there to this system? A. None B. Exactly 1 C. Exactly 2 D. Exactly 3 OE. Infinitely many F. None of the above If there are no solutions, enter "none" in each of the blanks. X = 2x - 6y -3x +9y y = = 7 If there is one solution, give its coordinates in the answer spaces below. If there are infinitely many solutions, enter x in the answer blank for x and enter a formula for y in terms of x in the answer blank for y. = : -12
13
Graph the systems of linear equations to determine the values of x and y that simultaneously satisfy both equations (if such values exist). Note: If the solution is an ordered pair, do not put spaces between the comma and the second value. If the solution is "no solution" or "infinitely many solutions," enter those words with spaces and spelled correctly.
Now, let's discuss the difference cases of solution to a given system of linear equations. There are three different cases: a) The system has exactly one solution (one set of solution). b) The system has no solution c) The system has infinitely many solutions. In this assignment, you will need to give an example a system of two linear equations (2 equations, 2 unknowns) for the three cases.
4 In the record books of Angorra, the following data was found: x - 2y = 6 Equation 1 -x + 4y = 6 .. Equation 2 Choose the most efficient approaches to solve the system given above. Add the equations. Multiply equation 1 by 2 and subtract the equations. Solve equation 1 for x and substitute the result in equation 2. Substitute -x + 4y for 6 in equation 1.
2. Consider the following system of linear algebraic equations: 2 3 x, 3 -4 6 x,= 4 %3D -2 6. a X3 where a and b are unknown real constants. Find the values of a and b such that the equations have i) ii) iii) unique solution, no solution, and infinitely many solutions.
According to projections through the year 2030, the population y of the given state in year x is approximated by State A: - 4x + y = 11,100 State B: - 140x + y = 7,000 where x = 0 corresponds to the year 2000 and y is in thousands. In what year do the two states have the same population? The two states will have the same population in the year.

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