For each matrix, consider the corresponding system of linear equations. How many free variables are there in the solution?[18.87a.One[1 00 36716.b. Two0 000[147C. None17[1-2d. One0 000

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Answered: For each matrix, consider the…

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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Find the augmented matrix for the following system of linear equations: -5x 16у + 4x 12y + + 97y -4 31x -31 || |||| | +
Please help!! Also, if possible give an explanation with the solution.
Set up a system of equations and then solve using inverse matrics. A manufacturer of portable tools has three sets, Basic, Homeowner, and Pro, which must be painted, assembled, and packaged for shipping. The following table gives the number of hours required for each operation for each set. Basic Homeowner Pro Painting 1.3 1.9 2.9 Assembly Packaging 0.8 1.5 1.9 0.6 0.6 1.3 If the manufacturer has 48 hours for painting per day, 32.1 hours for assembly per day, and 20.3 hours for packaging per day. How many sets of each type can be produced each day? The manufacturer can produce Basic sets, Homeowner sets and Pro sets per day.
4. 9 An ice cream shop sells small and large sundaes. One day, 30 small sundaes and 50 large sundaes were sold for $420. Another day, 15 small sundaes and 35 large sundaes were sold for $270. Sales tax is included in all prices. If x is the cost of a small sundae and y is the cost of a large sundae, write a system of equations to represent this situation. Peyton thinks that small sundaes cost $2.75 and large sundaes cost $6.75. Is Peyton correct? Justify your answer. Using your equations, determine algebraically the cost of one small sundae and the cost of one large sundae.
2. Solve the system of linear equation as follows: 2x1 + x2 4.x1 + 5x2 – 3x3 + 6x4 -2x1 + 5x2 – 2x3 + 6x4 4.x1+ 11x2 – 4.x3 + 8x4 x3 + 2x4 %3D 9 4 -

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For each matrix, consider the corresponding system of linear equations. How many free variables are there in the solution? [1 8. 81 a. One [1 0 3 67 1 6. b. Two 0. 0 00 0 [1 47 C. None 1 [1 -2 d. One 0 0 30 >