38 on Consider the linear system -22-61 +213 -11-57 +623 -211 -812 +673 71 +37 (0)...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
38 on Consider the linear system -22-61 +213 -11-57 +623 -211 -812 +673 71 +37 (0) Enter the augmented matrix of the system row-by-row in the input fields that follow (here and below, entries in each row should be separated by single spaces; please do NOT enter any symbol(s) to imitate the column separator): +71 +61 = 0 +6 +31 = 0 +1274 +975 = 0 -61-62 = 0 Gaussian Elimination (II) Perform the following elementary row operation(s) on the rows of the matrix in the previous part (1): R + R and enter the resulting matrix row-by-row in the input fields that follow: (1) Perform the following elementary row operation (s) on the rows of the matrix in the previous part (ii): R:- (-1) R and enter the resulting matrix row-by-row in the input fields that follow: (iv) Perform the following elementary row operation (s) on the rows of the matrix in the previous part(): R R+2R R3 R3+2R R = R R and enter the resulting matrix fow-by-row in the input fields that follow: (v) Perform the following elementary row operation(s) on the r of the and enter the resulting matrix row-by-row in the input fields that follow: the previous part (iv): R = (1/4) R (vi) Perform the following elementary row operation (s) on the rows of the matrix in the previous part (V): R: R-2R RR+2R and enter the resulting matrix row-by-row in the input fields that follow: (vii) Perform the following elementary row operation(s) on the rows of the matrix in the previous part (vi): R3:- (-1) R and enter the resulting matrix row-by-row in the input fields that follow: (vii) Perform the following elementary row operation(s) on the rows of the matrix in the previous part (vii): R = R R and enter the resulting matrix row-by-row in the input fields that follow: Now, judging by the last augmented matrix, the homogeneous linear system in question. does not have free variables. has free variables and hence R3=(-1) R has a unique solution has infinitely many solutions Jordan Elimination (ix) Perform the following elementary row operation(s) on the rows of the matrix in the previous part (viii): RR +6R R-R+ (5/2) R3 and enter the resulting matrix row-by-row in the input fields that follow: (x) Perform the following elementary row operation(s) on the rows of the matrix in the previous part (ix): R-R-5R and enter the resulting matrix row-by-row in the input fields that follow: Analyze the last augmented matrix to see that it is indeed in reduced row echelon form. General Solution (xi) Use (x) to obtain the general solution of the system, and enter it in the input fields below (If any of the equations is not necessary, please enter an asterisk in both input fields reserved for the equation): Fundamental Set of Solutions (xil) Finally, use (xi) to obtain the standard fundamental set of solutions (FSS) of the homogenous linear system in question, and then enter the coordinates of the vectors in the FSS similarly to of to 1,1,-2/1 0,1) (1, 1, -2/5, 0, 1 T If a particular vector is not necessary, please enter an asterisk in the input field reserved for it. If the system has no fundamental set of solutions (due to the absence of free variables), enter an asterisk in each input field. 3 ( (T 38 on Consider the linear system -22-61 +213 -11-57 +623 -211 -812 +673 71 +37 (0) Enter the augmented matrix of the system row-by-row in the input fields that follow (here and below, entries in each row should be separated by single spaces; please do NOT enter any symbol(s) to imitate the column separator): +71 +61 = 0 +6 +31 = 0 +1274 +975 = 0 -61-62 = 0 Gaussian Elimination (II) Perform the following elementary row operation(s) on the rows of the matrix in the previous part (1): R + R and enter the resulting matrix row-by-row in the input fields that follow: (1) Perform the following elementary row operation (s) on the rows of the matrix in the previous part (ii): R:- (-1) R and enter the resulting matrix row-by-row in the input fields that follow: (iv) Perform the following elementary row operation (s) on the rows of the matrix in the previous part(): R R+2R R3 R3+2R R = R R and enter the resulting matrix fow-by-row in the input fields that follow: (v) Perform the following elementary row operation(s) on the r of the and enter the resulting matrix row-by-row in the input fields that follow: the previous part (iv): R = (1/4) R (vi) Perform the following elementary row operation (s) on the rows of the matrix in the previous part (V): R: R-2R RR+2R and enter the resulting matrix row-by-row in the input fields that follow: (vii) Perform the following elementary row operation(s) on the rows of the matrix in the previous part (vi): R3:- (-1) R and enter the resulting matrix row-by-row in the input fields that follow: (vii) Perform the following elementary row operation(s) on the rows of the matrix in the previous part (vii): R = R R and enter the resulting matrix row-by-row in the input fields that follow: Now, judging by the last augmented matrix, the homogeneous linear system in question. does not have free variables. has free variables and hence R3=(-1) R has a unique solution has infinitely many solutions Jordan Elimination (ix) Perform the following elementary row operation(s) on the rows of the matrix in the previous part (viii): RR +6R R-R+ (5/2) R3 and enter the resulting matrix row-by-row in the input fields that follow: (x) Perform the following elementary row operation(s) on the rows of the matrix in the previous part (ix): R-R-5R and enter the resulting matrix row-by-row in the input fields that follow: Analyze the last augmented matrix to see that it is indeed in reduced row echelon form. General Solution (xi) Use (x) to obtain the general solution of the system, and enter it in the input fields below (If any of the equations is not necessary, please enter an asterisk in both input fields reserved for the equation): Fundamental Set of Solutions (xil) Finally, use (xi) to obtain the standard fundamental set of solutions (FSS) of the homogenous linear system in question, and then enter the coordinates of the vectors in the FSS similarly to of to 1,1,-2/1 0,1) (1, 1, -2/5, 0, 1 T If a particular vector is not necessary, please enter an asterisk in the input field reserved for it. If the system has no fundamental set of solutions (due to the absence of free variables), enter an asterisk in each input field. 3 ( (T
Expert Answer:
Answer rating: 100% (QA)
Solutions Step 1 Given a system of equation x1 x2 2 1 5x1 6x2 1 2 Gaussian Elimination i Augmented m... View the full answer
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...
-
The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-4. Ivan and Irene paid the following in 2012 (all by check or can otherwise be...
-
The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-6. On December 12, Irene purchased the building where her store is located. She paid...
-
You have been asked to manage a $3 million university endowment fund, which is used to fund the additional salary stipend for 5 endowed chair positions. The stipend for each chair is $30,000 (for a...
-
A thin layer of ice (n = 1.309) floats on the surface of water (n = 1.333) in a bucket. A ray of light from the bottom of the bucket travels upward through the water. (a) What is the largest angle...
-
What is the Earth-Centered, Earth-Fixed (ECEF) model and how it is used?
-
The accounts and June 30, 2007, balances of Cromwell Company are arranged in no particular order: Requirements 1. Prepare the company's classified balance sheet in account format at June 30, 2007. 2....
-
Compute the cost of capital for the firm for the following: a. Currently bonds with a similar credit rating and maturity as the firms outstanding debt are selling to yield 8 percent while the...
-
Would it be a good time to buy stocks when the S&P500 Index PE is 20 times? Why or why not?
-
Wayland Custom Woodworking is a firm that manufactures custom cabinets and woodwork for business and residential customers. Students will have the opportunity to establish payroll records and to...
-
A rectangular field is 0.3 kilometers long and 0.2 kilometers wide. What is the area of the field in square meters? Do not round your answer. 2 m X Conversion facts for length 1000 millimeters (mm) -...
-
Carol had a universal life insurance policy with a death benefit of $100,000. The policy had a cash value of $18,000. They noticed that she had marked death benefit option B and made Michael the sole...
-
Madison purchased a new car for $23,000. She was allowed $2,000 for her trade in and financed the remainder over 48 months at a rate of 4% per year. How much is her monthly payment?
-
According to the instructions on the tax form, the tax on an income greater than $45,625 and less than $98,631 is $5467.25 plus 0.25 times the amount over $45,625. Arrange the steps in order that is...
-
The company i have is Cole Group Limited. The competitors are Woolworths, Metcash and Endeavour. the ratios are Current Ratio, P/E, Roa and ROE i do not know how to go about this assignment. 4.3 4.4...
-
The random variable x has the following probability distribution. x f(x) 0 0.15 1 0.20 2 0.25 3 0.25 4 0.15 (a) Is this probability distribution valid? Explain and list the requirements for a valid...
-
You are valuing a company as of the end of Year 0. The company is privately owned and 100% equity financed. The companys free cash flow for the current year, Year 0, is $40 million, and management...
-
The percentage of completion and completed contract methods are described in the FASB ASC. Search the codification to find the paragraphs covering these topics, cite them, and copy the results.
-
Solve the following linear recurrences. (a) xk+2 = 2xk - xk+1, where x0 = 1 and x1 = 2. (b) xk+2 = 6xk - xk+1, where x0 = 1 and x1 = 1.
-
Let A, B, and C denote n n matrices. Using only Theorem 4, show that: (a) If A and AB are both invertible, B is invertible. (b) If AB and BA are both invertible, A and B are both invertible. (c) If...
-
In each case find U-1 and compute dim U1 and dim U1 (a) U = span{[l 1 2 0], [3 -1 2 1], [1 -3 -2 1]} in R4 (b) U = span{[l 1 0 0]} in R4 (c) U = span{l, x} in P2 with (P. q) = P(0)q(0) + p(1)q(1) +...
-
True or False. The half-power points denote the values of frequency ratio where the amplification factor falls to \(Q / \sqrt{2}\), where \(Q\) is the \(Q\) factor.
-
True or False. The response is always in phase with the harmonic forcing function in the case of hysteresis damping.
-
True or False. The amplitude ratio attains its maximum value at resonance in the case of viscous damping.
Study smarter with the SolutionInn App