5

You are asked to solve a linear system Ax =b where A is an 700 x 700 invertible matrix with condition number K(A) = 9,900 Suppose that the coefficient matrix A is k...

Question

You are asked to solve a linear system Ax =b where A is an 700 x 700 invertible matrix with condition number K(A) = 9,900 Suppose that the coefficient matrix A is known to 8 significant figures and the right-hand-side vector b is known exactly: Give an estimate on the relative error in the computed solutionSE-5 0.010 2E-16 10E-9

You are asked to solve a linear system Ax =b where A is an 700 x 700 invertible matrix with condition number K(A) = 9,900 Suppose that the coefficient matrix A is known to 8 significant figures and the right-hand-side vector b is known exactly: Give an estimate on the relative error in the computed solution SE-5 0.010 2E-16 10E-9



Answers

Determine the solution set to the sys$\operatorname{tem} A \mathbf{x}=\mathbf{b}$ for the given coefficient matrix $A$ and right-hand side vector b. $$A=\left[\begin{array}{rrrr} 1 & -1 & 0 & -1 \\ 2 & 1 & 3 & 7 \\ 3 & -2 & 1 & 0 \end{array}\right], \mathbf{b}=\left[\begin{array}{l} 2 \\ 2 \\ 4 \end{array}\right]$$

Number one to get the again van use. So we remind that, uh, determined Think seven London and zero Get this tree negative seven minus. Amanda would be equal to zero. Eso uh, we have negative Syrian minus done. The negative seven minus one equals zero. So Lunda is equal to negative seven and negative seven. Ah, so hints that London reporter Negative seven. Ah, we can say that the algebraic multiplicity about the publicity. It's April 2. Ah, work long guys equals seven Negative. Seven a x. It's a quick too Here, Negative three zero and zero x one x two Get a quick too Europe and you From here we can get that X one is equal to zero. So the hike into space, uh, is equal. Ah, explain and extreme. It's one of exclude Ah hiss x one. It's equal to you. So is equal to zero and x to as x two uh belong to who are s So what? That I mentioned off the I in space. So where that I mentioned off the I get space is equal to one. Ah, since the metrics that don't have to think I convey idiots. It is not a non detective and a has only one linear independent again. Vector A is effect. So we can say that Ah a That's only one in your independent I get back. I am back there. Uh, school A It's effect.

Problem number at Well to detect the again values. We say that that determined off a minus Lunda is equal to zero. So seven miners Lunda eight and view no getting AIDS. No, never mind. Minus Lunda and you 66 and negative one minus is equal to you. From this determinant, we, ah gain the longer cross one que is equal to zero. So long break through and get the warrant. They get one and they get support. We're ah longer Isaac were turning it one. And as we know that a minus Lunda time in the unity not a blind by the factory is equal to zero. But you give that everyone or for times, be one minus four time with me too. A blood three times Every three is equal to zero. So we get that re vector is equal to buy 11 of you plus s negative three The room for we're by us belongs to the are so the director is equal toe 11 and ah dear Negative 304 for the bases. Ah, the I in space eso that I mentioned off the agony space e is equal to ah two is not equal to three. That's why we can say that. And as the effective

Indication given system of equations are That is 3.1 next Plus six. white minus 8.700. Mhm Is equal to 1.5. Second equation is that is 4.1 next -5 one way plus 0.2. There Is equal to 2.1 And 3rd equation is 0.66 plus 1.1. Why -7.4 dead Is equal to 3.9. Now in the cushion it is asking that first right. The given system in med techs forum and my texas equation given that is a X plus B 2nd. We it is asking to find the inverse matrix means universe by using the computer. And In these metrics in West Metrics limits have up to four decimal place. And the third last it is asking to find the solution of system of equation by using metrics equation that is X. Is equal to in what's big. And you can also use a calculator and it also said dead in solution the Where you will be up to four decimal place. So no, I will try to write the answer you step by step. So first I will write the given the system of equations in matrix form. So given metric situation is that is X is equal to be well it will be which is called a coefficient metrics and where you will be that is inside the elements are coefficient of X, Y jail. It will be written as that is 3.1, Then 6.7, then minus minus 8.7. In the second element south, That is 4.1, then minus 5.1, Then 0.2. and in the 3rd row elements are written as 0.66 0.6 At 1.1 Then -7.4. No year X is there when it takes off three reliable. That is Xy dead and uh be easier variable B geometrics of 1.5 2.1 And 3.9. So no. Using the metric situation, the system will be written in the metrics form that is X means 3.16.7 -8 months, seven, 4.1 -5.1 zero point To then 0.6 1.1 then -7.4. Okay, in terms of metrics ex miss metrics of Xy jet will be equal to metrics of B means 1.5 2.1 3.9. So this is the self all first part A. Now I will try to find the part B in which it is asking to find the inverse matrix means N was by using calculator. So here I will find the answer of B by using this most metrics calculator and in putting all the data. So this is a s most metrics calculator. And as you see the I have made a metrics Ordinary status he grow three which is given in the execution. No, I will write the elements one x 1. So in the first row the element is status, This is 3.1, then 6.7, then minus 8.7. Then in the 2nd row, elements are, It is 4.1, then minus 5.1, then judo point two. Then in the 3rd row, elements are that is 0.6, then 1.1 Then -7.4. Now click the enter and now we have to find the inwards of e metrics means the universe. So as you see in the result, I get the universe. Now in the break it the agreements have more decimal place, but in the communities are seen to round off to four decimal place. So looking the result, I will say that a in which will be equal to in the first row elements are that is 0.1474, Then 0.1572, then -0.1691. In the second row elements are that is 0.1197, then zero six, then minus 0.14- six. And in the 3rd row elements out at least 0.0297 And 0.0024 And then last -0.1700. So all I can say that it will be written as the universe will be equal to. That is after looking the result which I sold in the by using the death most metrics calculator. So answer the status in the first elemental 0.1 Soul 74. Then 0.1572, Then zero 1691. Then 0.1 in second row elements are that is European 1197, then minus 0.06 96 then -0.14 2 6. And in the cardio elements are zero point. Do you do 297 And 0.0024? Then zero 1700. So this is the answer for part B. No. I will try to find the ourself for part C. In which it is asking to find the solution by using metric situation. So write this equation given that is X. Is equal to A. In what's be. So here we have to put value of X. Matrix is on the left side and on right side we have to multiply inwards metrics and be metrics. So and in the community also said that we can use the calculator. So I am using the day's most mattress calculator. So so this is a death most metrics computer and I had to get the in was bye for party part B. So this is the value of the universe. No right. The metrics be They have ordered that is three close 1 And the elements are that his first element 1.5, Then 2nd 2.1 And third that is 3.9. No click the enter then then what we have to get friendlies. A universe B. So a universe times of B. So as you see in the back of the elements of more decimal place. And in the community saying that we have to round off to four decimal place. So after on round off the it must be equal to in the record, the elements are daddy's will be after rounding off rounding the remains. Our first element will be mine ist 0.1081, then -0.5: 2 7 and -0.6135. Or I can say that it will written as that is X is a matrix of Xy jed is equal to a must be which I get by using the there's most metrics capital and the value is status. Elements are first element is zero 1081, then -0.5 227 The an -161 35. No next step is missed. The elements on both sides. So I can say that X will be equal to -0.1081. Why will be equal to minus 0.5 227 and God will be equal to minus. Do you know point 6135? So this is a solution of given system of equation by using my text equation. Hence, I had sold the all parts means completed. Elocution. Thank you.

To a question asked to find a solution off a X equal. Be first. We need to change a given system into all romantic and metrics form for row to we can do to times roll. One minus wrote you and for over three we can do three times. Roll one minus roastery Copyright one. But for rosary, we can do row to minus three times a role. Three Every time when we see zeros here, but a constant. The number here, which means is this is a better room. The matrix is inconsistent, which means there's no solution.


Similar Solved Questions

5 answers
Mon May hT2so+607"}4J 6L [5arematic
Mon May h T2so+6 0 7"}4 J 6L [5 arematic...
5 answers
Which of the following is correct? Write the correct symbol if needed. (4.1)a. copper, $mathrm{Cp}$b. silicon, SIc. iron, $mathrm{Fe}$d. fluorine, $mathrm{Fl}$e. potassium, $mathrm{P}$f. sodium, Nag. gold, Auh. lead, $mathrm{PB}$
Which of the following is correct? Write the correct symbol if needed. (4.1) a. copper, $mathrm{Cp}$ b. silicon, SI c. iron, $mathrm{Fe}$ d. fluorine, $mathrm{Fl}$ e. potassium, $mathrm{P}$ f. sodium, Na g. gold, Au h. lead, $mathrm{PB}$...
5 answers
At $298 mathrm{~K}$, a sealed 750 -mL vessel contains equimolar amounts of $mathrm{O}_{2}, mathrm{H}_{2}$, and He at a total pressure of $3.85$ atm. What is the partial pressure of the $mathrm{H}_{2}$ gas?
At $298 mathrm{~K}$, a sealed 750 -mL vessel contains equimolar amounts of $mathrm{O}_{2}, mathrm{H}_{2}$, and He at a total pressure of $3.85$ atm. What is the partial pressure of the $mathrm{H}_{2}$ gas?...
5 answers
Find the sum of the measure of the angles and the degree of each angle
Find the sum of the measure of the angles and the degree of each angle...
5 answers
Problem 3.10. Consider the function f , where 22 if c € Q f(c) -3 if c & Q Calculate the upper and lower Riemann sums based on an arbitrary partition P = {xo; TEn} of [0,1]. Explain how do you use the density phenomenon of real numbers in your calculations.
Problem 3.10. Consider the function f , where 22 if c € Q f(c) -3 if c & Q Calculate the upper and lower Riemann sums based on an arbitrary partition P = {xo; TEn} of [0,1]. Explain how do you use the density phenomenon of real numbers in your calculations....
5 answers
Project number 4 Oh ONI
Project number 4 Oh ONI...
5 answers
Before the formation of a root nodule, which partner secretes a Nod factor, the plant or the bacterium?
Before the formation of a root nodule, which partner secretes a Nod factor, the plant or the bacterium?...
5 answers
The chemical Iormula ol acetarinophen I5 CgHgNOz: Is acetaminopren an Crement, compound @r & mixture? Explanyour choice and wry the Othor tiw choices are Incorrect Which sample coniains more atorns , one mole ol nitrogen gas or ane rnole of carbor dioxide '915? Or d they boxh contain [ same number ol aloms? Explain yOlr answer
The chemical Iormula ol acetarinophen I5 CgHgNOz: Is acetaminopren an Crement, compound @r & mixture? Explanyour choice and wry the Othor tiw choices are Incorrect Which sample coniains more atorns , one mole ol nitrogen gas or ane rnole of carbor dioxide '915? Or d they boxh contain [ same...
1 answers
Two flasks, each with a volume of $1.00 \mathrm{L},$ contain $\mathrm{O}_{2}$ gas with a pressure of $380 \mathrm{mm}$ Hg. Flask $\mathrm{A}$ is at $25^{\circ} \mathrm{C},$ and flask $\mathrm{B}$ is at $0^{\circ} \mathrm{C}$. Which flask contains the greater number of $\mathrm{O}_{2}$ molecules?
Two flasks, each with a volume of $1.00 \mathrm{L},$ contain $\mathrm{O}_{2}$ gas with a pressure of $380 \mathrm{mm}$ Hg. Flask $\mathrm{A}$ is at $25^{\circ} \mathrm{C},$ and flask $\mathrm{B}$ is at $0^{\circ} \mathrm{C}$. Which flask contains the greater number of $\mathrm{O}_{2}$ molecules?...
5 answers
Change from rectangular to cylindrical coordlnates. (Let r 2 0 and 0 < 0 < 21,) ~3(-3,-3v3, 1)
Change from rectangular to cylindrical coordlnates. (Let r 2 0 and 0 < 0 < 21,) ~3 (-3,-3v3, 1)...
1 answers
Consider all rectangles with an area of 200 $\mathrm{m}^{2} .$ Let $x$ be the length of one side of such a rectangle. (a) Express the perimeter $P$ as a function of $x$ . (b) Find the dimensions of a rectangle whose perimeter is 70 $\mathrm{m}$ .
Consider all rectangles with an area of 200 $\mathrm{m}^{2} .$ Let $x$ be the length of one side of such a rectangle. (a) Express the perimeter $P$ as a function of $x$ . (b) Find the dimensions of a rectangle whose perimeter is 70 $\mathrm{m}$ ....
5 answers
9.An examination consists of two papers, Paper 1 and Paper 2_ The probability of failing in Paper 1 is 0.3 and that in Paper 2 is 0.2 Given that student has failed in Paper 2,the probability 0f failing in Paper 1 is 0.6 Then the probability of student failing in both the papers is equal to: 0 (3 Points)0.50.060.120.18
9.An examination consists of two papers, Paper 1 and Paper 2_ The probability of failing in Paper 1 is 0.3 and that in Paper 2 is 0.2 Given that student has failed in Paper 2,the probability 0f failing in Paper 1 is 0.6 Then the probability of student failing in both the papers is equal to: 0 (3 Poi...
5 answers
Deew L f # L 1 L 1 1 1 1 1 1 3 1 1 1 1 V 7 1 V 5
Deew L f # L 1 L 1 1 1 1 1 1 3 1 1 1 1 V 7 1 V 5...
5 answers
Question 7 (10 points) The probability of Chester making Iree throw in the championship basketball game is 80%, and each throw is independent of his last throw: Assume that Chester attempts five free throws during the game_ What is the probability that he will make more than four of his free throws during the game? Round decimal places.
Question 7 (10 points) The probability of Chester making Iree throw in the championship basketball game is 80%, and each throw is independent of his last throw: Assume that Chester attempts five free throws during the game_ What is the probability that he will make more than four of his free throws ...
5 answers
The sludent council at a high school consists of 12 seniors , juniors sophomores, and ireshmen_ Five members Irom Ine councll are chosen at random to be on committee . Find the number committeos that contain exactly sonlors and no freshmenThe number Is
The sludent council at a high school consists of 12 seniors , juniors sophomores, and ireshmen_ Five members Irom Ine councll are chosen at random to be on committee . Find the number committeos that contain exactly sonlors and no freshmen The number Is...
5 answers
Use calculator to find = decimal approximation for the following trigonometric function. sec 35*12'B8c 35912' ~ (Simplify your answer Type an integer or = decimal. Round to eight decimal places as needed )
Use calculator to find = decimal approximation for the following trigonometric function. sec 35*12' B8c 35912' ~ (Simplify your answer Type an integer or = decimal. Round to eight decimal places as needed )...
5 answers
Given f (x) = 5 - $ find all values of in the open interval (1,4) such that the average rate of change is equal to the instantaneous rate of change: marks)
Given f (x) = 5 - $ find all values of in the open interval (1,4) such that the average rate of change is equal to the instantaneous rate of change: marks)...

-- 0.039720--