Consider the following triangular system: where b is a real number. (x+y+z+w = 2 -6x+5w 3z-w...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Consider the following triangular system: where b is a real number. (x+y+z+w = 2 -6x+5w 3z-w 2w = b2 "I -4 a. For what value(s) of b, if any at all, does this system have a unique solution? Briefly justify your answer with a short explanation or short calculation. b. For what value(s) of b, if any at all, does this system have infinitely many solutions? Briefly justify your answer with a short explanation or short calculation. c. For what value(s) of b, if any at all, does this system have no solution? There's no need to justify your answer to (c) as it will be the complement of your answers to (a) and (b). Consider the following systems of square linear systems: x+3y-z =4 a. 4x-y+2z =8. (2x-7y+4z = -3 x+3y-z =4 b. 4x-y+22 = 8. (2x-7y+4z = 0 x+3y-z =4 C. 4x-y+2z = 8. (2x-7y+6z=0 Which of these systems has no solution? (There is only one.) What are the solutions of the remaining two systems? Exercise 1. (CS1.1) Component Skills Exercises A chemist must determine the coefficients x; (for 1 j 7) that balance the reacti x1PCH4 + x2KMnO4 + 3H2SO4 x4PCHO2 + 5K2SO4 + x6MnSO4 + x; -> In order to balance this reaction, there must be an equal number of each element the reaction. Use this information to derive a linear system satisfied by the unkn xj. What are the dimensions of this system? Remark: Please derive an equation for each element. Note that some of your be redundant. For sake of consistency, keep these redundant equations in your syst Exercise 2. (CS1.2) Consider the following triangular system: x + y + z = 2 a22y+2% = b . 3z = 9 a. Suppose a22 = 1 and b = 6. What is the solution of this system? b. Suppose a220 and b = 6. What is the solution of this system? c. Suppose a220 and b = 0. What is the solution of this system? Exercise 5. (CS1.3) Express the linear system in Exercise 1 in matrix-vector form and as an augmented matrix. Exercise 6. (CS1.4) From Olver and Shakiban, complete Exercises 1.2.7(b), (c), (f), and (h). For (h), I is the ap- propriately sized identity matrix. Remark: Unless very special circumstances are at play, remember AB + BA. Consider the following triangular system: where b is a real number. (x+y+z+w = 2 -6x+5w 3z-w 2w = b2 "I -4 a. For what value(s) of b, if any at all, does this system have a unique solution? Briefly justify your answer with a short explanation or short calculation. b. For what value(s) of b, if any at all, does this system have infinitely many solutions? Briefly justify your answer with a short explanation or short calculation. c. For what value(s) of b, if any at all, does this system have no solution? There's no need to justify your answer to (c) as it will be the complement of your answers to (a) and (b). Consider the following systems of square linear systems: x+3y-z =4 a. 4x-y+2z =8. (2x-7y+4z = -3 x+3y-z =4 b. 4x-y+22 = 8. (2x-7y+4z = 0 x+3y-z =4 C. 4x-y+2z = 8. (2x-7y+6z=0 Which of these systems has no solution? (There is only one.) What are the solutions of the remaining two systems? Exercise 1. (CS1.1) Component Skills Exercises A chemist must determine the coefficients x; (for 1 j 7) that balance the reacti x1PCH4 + x2KMnO4 + 3H2SO4 x4PCHO2 + 5K2SO4 + x6MnSO4 + x; -> In order to balance this reaction, there must be an equal number of each element the reaction. Use this information to derive a linear system satisfied by the unkn xj. What are the dimensions of this system? Remark: Please derive an equation for each element. Note that some of your be redundant. For sake of consistency, keep these redundant equations in your syst Exercise 2. (CS1.2) Consider the following triangular system: x + y + z = 2 a22y+2% = b . 3z = 9 a. Suppose a22 = 1 and b = 6. What is the solution of this system? b. Suppose a220 and b = 6. What is the solution of this system? c. Suppose a220 and b = 0. What is the solution of this system? Exercise 5. (CS1.3) Express the linear system in Exercise 1 in matrix-vector form and as an augmented matrix. Exercise 6. (CS1.4) From Olver and Shakiban, complete Exercises 1.2.7(b), (c), (f), and (h). For (h), I is the ap- propriately sized identity matrix. Remark: Unless very special circumstances are at play, remember AB + BA.
Expert Answer:
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
Posted Date:
Students also viewed these mathematics questions
-
In Exercises find the derivative of the function. y = x-4-2 arcsec X 2 2 < x < 4
-
thank you Customers arrive at a supermarket in accordance with a Poisson process with rate 10 per minute. The amount of money each customer spends is a random variable with mean R150 and standard...
-
State Einstein's postulates of the special theory of relativity. ii. Write down Einstein's mass-energy equivalence formula. iii. In the case of two inertial frames of reference, S' moving at a...
-
Right-tailed test; = 0.025 Find the critical z values for the given conditions. In each case assume that the normal distribution applies, so Table A-2 can be used. Also, draw a graph showing the...
-
Case Credit Corp. (Case) finances the sale of farm equipment to farmers. Day bought farm equipment financed by Case, yet Day never actually signed the sales contract. Instead, an employee of Case...
-
Diagnostic Services Inc. (DSI) is a new company. It has been in business for only one year, offering diagnostic services to physicians in the Tampa/St. Petersburg, Miami, and Orlando markets. DSI...
-
A Pentecostal nurse claims she was constructively discharged after refusing to assist in medical procedures she considered to be abortions because of her religious beliefs. She was initially...
-
Bell Canada stocks a certain switch connector at its central warehouse for supplying field service offices. The yearly demand for these connectors is 15,700 units. Bell estimates its annual holding...
-
Why is communication very crucial in team building? Outline some barriers to effective communication, and share any life experience you've had over the years.
-
Discuss how a firearm and ammunition use both potential and kinetic energy.
-
How might the self-fulfilling prophecy work in a positive sense? A negative sense? which is more common, and why? How can negative thoughts like this be realistically managed?
-
Direction: Make an essay about festival dance, chose one from the given questions below. Write your answer in a separate sheet of paper. Processing questions: 1. Why is there a need for festivals?...
-
Describe one type of role-play technique you could use in a specific group setting. Explain who would benefit from this technique and why. Toseland, R. W., & Rivas, R. F. (2017). An introduction to...
-
Suppose that a manager is following a base stock policy where the optimal inventory position is 10. Assume the component lead time is 2 days. At the end of day 1, there is no ordered units yet to be...
-
Provide an overview of a forecasting technique or forecasting procedure: develop a specific forecasting model from those that are included in chapter 5 of the textbook. Apply the forecasting model to...
-
Let X be a random variable taking on values a1, a2, . . . , pr with probabilities p1, p2, . . . , pr and with E(X) = μ. Define the spread of X as follows: This, like the standard deviation, is a...
-
The overall process of creating a capital budget proposal has a lot of similarities to writing a business plan for a start-up company. Describe three aspects of the similarities between a budget...
-
There are three general categories of capital budget scenarios: replacement, expansion, and investment in a NewCo. Describe the overall decision-making context for each. How do they draw on similar...
-
In analysis, some focus seems to be on the need for NPV equations to be applied to projects that are mutually exclusive. But in practice we find that the lines are blurred in capital budgeting....
Study smarter with the SolutionInn App