5

Consider linear system whose augmented matrix is of the form8 + 1where B € R For which of the following value or values of 8,this system is consistent?Select ...

Question

Consider linear system whose augmented matrix is of the form8 + 1where B € R For which of the following value or values of 8,this system is consistent?Select one;

Consider linear system whose augmented matrix is of the form 8 + 1 where B € R For which of the following value or values of 8,this system is consistent? Select one;



Answers

Find all values of $k$ for which the given augmented matrix corresponds to a consistent linear system. (a) $\left[\begin{array}{llr}1 & k & -4 \\ 4 & 8 & 2\end{array}\right]$ (b) $\left[\begin{array}{lll}1 & k & -1 \\ 4 & 8 & -4\end{array}\right]$

All right. So, we're looking for all values of K. That would make this matrix correspond to a consistent linear system. So in order for a system to be consistent, we want to have either one solution or influence infinitely many. So that means when you end up with a one here and a number here, there'll be a unique solution. And if you get all zeros, you have infinitely many solutions and it would be inconsistent if we have zeros and then a number and I can't get my thing to go down. Let's see. Come on. Just a great here. Let's see here. You got a zero here and numbers here, then it is not. It's going to be inconsistent. No solution. So we're what to start off by getting zero on the bottom. So we can do Yeah. Row go. Well. Well then we can multiply that. Bad cheese. And then added to routine to be your new routine. Sarah Palin will be the same. Mhm. And then, yeah, it's a pleasure to you by Well, one x 2, we'll give you six plus minus 630 Mhm. Two times negative four is negative eight plus 80 And then we have K Times to use 2K. And we have to keep this bike. Yeah. Yes. Yeah. Okay. So you can receive it here. You get zero here. Okay. And in order for it to be consistent, has to be we're gonna have to have a seat right here. So when two gay plus five Equals zero, then it will be consistent. You just saw that. So when K equals negative five or 2, that's when it would be a consistent system. Hey? Yeah. Yeah. Alright. For part B. We want to get leading one here So we can multiply road one times one over K. So your new red one. See you in it with one and 1 over K. and -2 over. Okay. And you second rate will stay the same. And we think All right, I'm gonna get a zero Where the four is. We're gonna multiply row one times negative four plus routine. But we'll give you your new road to so when when will stay the same one? Whenever. Kay. Okay. You have to over. Hey, Sorry. Sorry. Thanks dad. Whenever Okay, negative two. Okay, that stays the same. And then row one times negative four is negative four plus 40 Do you have negative four over K anymore? Mhm. Plus -1 -1. And then you have negative for times negative two of. Okay. Which will be positive. Ak plus cheap. Are you know, order for this to be consistent? Let's just see. Let's see chemicals four. Okay. Okay. Okay, equals four. We're actually gonna make him negative for so that we can turn him an easy ride right here. Yeah. Let's take a who's in here for That is a negative for Sorry. All right. So, you plus I didn't get negative for over negative 4 -1. This is a spark Which turns into 1 -1, which equals zero. Okay. So you have a secret there. So, let's see what happens when you play in. Yeah. Native for over here. Yeah. Right here. Yeah. You get eight over negative four plus two, which gives you negative two plus two equals zero. So, they would both equal zero. Which implies that there are infinitely many many solutions. Sorry, my hands. It's not very good, but it's been infinitely many solutions. Mhm. So, K can equal any any number. Mhm Yeah. Many. It's OK. Can be any real number.

This is a question normal 18 or the given? Augment. Admit it's we had, right, the system off equation. So for the faster we can right here three x and they get you do Why less Why's that? Is according to no for the second rope we can right here. Eggs. Plus here we has it also right here. Zero. Why here? We have negative ones of your negatives That has equalled wonder I said we have negative treat right now from the car drove here has 0002 American right here dude awakes unless Syria white plus serious that is equal to underestimate rage. So here what for any really off X y said zero x plus zero y zero That cannot be called Do it right. So we can say that the system is inconsistent. Right? So your system has no solution. Thank you.

For this problem, we're going to solve the set of linear equations by using gassy elimination, which means we want to simplify our matrix into reduced echelon form. So our first step for doing that is to write out The Matrix that corresponds to the set of equations up were given to us. So the first equation reads. Zero x one plus x two plus three x three minus two x four is equal to zero. The 2nd 1 reads to x one plus x to minus four x three plus three x or is equal to zero. The 3rd 1 reads to x one plus three x two plus two x three minus x four equals zero and the last equation that were given reads negative four x one minus three x two plus found X three minus four of four is equal to zero. The first step that we're gonna do is we're going to cancel out this term to make it a zero. We can do that by setting our two equal to our two minus r three, and that is going to give us the following matrix. First row is gonna say the same. The second row is going to become zero negative, too negative, six or zero and then the other two rows are going to stay the same. Okay, Our next up is going to be to make the second row, actually a row of all zeros and we can see that we could do that pretty easily by looking at how the first row is pretty much just a scaler of the second World. So two kids love this road. They call Ciro's ruins that are too. People Thio two are one plus are too. When we do that, we get the following major. So again the first roast is the same. The second row is gonna cancel out completely, given the substitution into the equation for our two that we wrote. And again the third and fourth rows are going to stay the same. Okay, next up, we want to make this entry or negative for injury a zero. And when we do that, this will be the only entry in the column. That's not zero, which is good for the form that we want to get into. So in order to eliminate that, we're gonna set our four equal to to our three. Those are for once we do that, we get following matrix. So again, these rose rows one through three are gonna say it seems we're not doing anything to them. And row for is going to become zero three non negative six and zero by the equation given next up, we want to cancel out this entry right here. That's gonna be our next step. So in order to do that, we just have to do some subtraction and we have to say, or three is equal to are three minus are for and that is gonna give us the following matrix. The first row is gonna stay in the same that there was going to stay the same or Robles heroes. Our third row is is going to become to zero negative seven, 50 bug subtraction. The question on the other page and our last row is gonna say the same. So 039 negative. Six and zero. Oh, it so next up, what we want to do. ISS We want to cancel out most of this road because, like a difficult operation that we already did, we can see that Row one is pretty much just a scaler multiple of row three, so that should be pretty easy to cancel out. So what we're gonna do is that our four people to our four minus three are one. Well, we do that. We're going to get then used to roast, stay the same, and this last row is going to become a row of all zeros. So now what we want to do is we want to put our all zero rose at the very bottom of the Matrix. So one of them is already in at the bottom and the other one right here, we can just switch with the road below it. So that's gonna be our two is gonna be ableto the current are three, and our three is gonna become equal to the current are too. And this gives us the following matrix. Okay, Next up, we want to switch these two rows with each other because as per rules of reduced echelon form, we want to make sure that the left most leading entry is at the top of the matrix. So are one is going to war too, and our two is going to become a recurrent or one that's gonna give us this following matrix. Then again, we have are all zeros on the very bottom. Okay, so now our next step is we want to divide are one by two. So that this leading entry is a one which matches the form that we want to put our Matrix into. So are what is he? Will one have times are one, and that is going to give us the following matrix. That's gonna give us 10 negative seven halfs. But house zero our second row's gonna say the same. So one 013 to 0 and then our rose three and roast. We're also gonna say the same. Okay, so now we're ready to solve for our variables. So we're gonna label this X will in x two x three explore so we can see the columns are correspondent What variables. And we can also see that ex one next to these variables. Herbal pivot values. So that means that our free variables rx three the next four. So what that means is we want to solve for X one and X two in terms of x three, next four. So we're gonna start with the first row. So are one reads That's one plus zero x two minus seven halfs x three. Let's buy a house. Explore is equal to zero X. You cancels out because it's coefficient zero and we're left with x one minus 7/2 x three. Let's buy half explores equal to zero and we want to solve for X one in terms of our free variables. So to do that, we just put the other free variables on the right hand side and we get that X one is equal to seven. House X three minus five halfs, that's for okay. Now we're going to go to our second row and that reads zero x one plus x two plus three x three Bonus two x four is equal to zero and from there not cancels. We're gonna sell for X two in terms of x three and explore so x two equals negative three x three close to export. So we sell for variables. And if you want to write that in a vector form, we can do that by writing ex one. Next to is equal two next three times the following vector. We have a seven. How? Spector at a negative three. Er sorry. Seven house and negative. Three is sailors. And then we're going to add that to explore times following vector, uh, native five house and two. And we just got these numbers from these entries here. So the X three terms here and here We plugged those in right here and our export values. We got them from here and here. I put them in here.

With your question over 20 as we can see here that it's no by ordinary at the start column, right? And when did I said We have year old side where we can say Here the system is consistent. System has infinitely many solutions? No. From the first row, we can write our first equation that is your X plus era y negative Do that the God of Seven. Right? So here X plus Syria White negative Tuesday is a cordial seven. From the second row, we can write our second equation that is Syria X plus y plus four that is a golden three of your zero X. That's why, plus force that is he called with three. Then here. That is a gold of that. Which means or that he's three very about right now your coefficient off y zero. But we can *** let the zero item, but your ex negating to that is according seven only. And here zero x studies zero. But we can like Let's your all right only white last more. That is a quote, right? No subject X indicia questions of your ex physic world, say one last Tuesday and subject white Indus Aggressions of your wife is 1/4 3 negative forces and the basic work exact. This is our pre valuable Well, the general solution is that he's ex wives, that liquidity we are extent is seven plus schools that why that is three minus for that And that is a chord. Isn't that is any real number said this is our potential Do show. Thank you.


Similar Solved Questions

3 answers
Find invertible P ad diagonal D such thatP-'AP = D, ud uSC thosc mnabrices 4o calculale AI4
Find invertible P ad diagonal D such that P-'AP = D, ud uSC thosc mnabrices 4o calculale A I4...
5 answers
A table of values for f.g.f and , g' is given: Alr) g(*) f) 8 )(10 'pts ) Find (f 0g)"() .b. (10 'pts ) Find
A table of values for f.g.f and , g' is given: Alr) g(*) f) 8 ) (10 'pts ) Find (f 0g)"() . b. (10 'pts ) Find...
5 answers
How do you explain the fact that skeletal muscle has an optimal length? Why does contraction initiated at non-optimal lengths produce less forceful contraction?
How do you explain the fact that skeletal muscle has an optimal length? Why does contraction initiated at non-optimal lengths produce less forceful contraction?...
5 answers
9070ddccn MJetcoAaBb(CllliZn #0 i Metstul =Men 584 ottntLebaat
9070 ddccn MJetco AaBb( CllliZn #0 i Metstul = Men 584 ottnt Lebaat...
5 answers
Question 12 (1 point) The diagram below demonstrates which of the rules for filling orbitals being br IncorrectThe Pauli Exclusion Principleb) The Aufbau PrincipleHund's RuleThe Uncertainty PrincipleZeeman Effect
Question 12 (1 point) The diagram below demonstrates which of the rules for filling orbitals being br Incorrect The Pauli Exclusion Principle b) The Aufbau Principle Hund's Rule The Uncertainty Principle Zeeman Effect...
5 answers
Determine if the lines $mathbf{r}_{1}(t)-(2,1,1)+t(-4,0,1)$ and $mathrm{r}_{2}(x)-$ $(-4,1.5angle+x(2,1,-2)$ interxect and, if $mathrm{xo}$, find the point of intersecfion
Determine if the lines $mathbf{r}_{1}(t)-(2,1,1)+t(-4,0,1)$ and $mathrm{r}_{2}(x)-$ $(-4,1.5 angle+x(2,1,-2)$ interxect and, if $mathrm{xo}$, find the point of intersecfion...
5 answers
Needea lor Ihi uuetlnnComplete the table below for calculating the molecular weight of the compound 2,3-dimethyl-2-butanol = shown in the Fball . sticklabelsAtomAtomic Weight amlatomAtomsWeight in compound muatomcAmW atomatomsamuamWalomatomsaMumolecular weight of 2,3-dimethyl-2-butanol
needea lor Ihi uuetlnn Complete the table below for calculating the molecular weight of the compound 2,3-dimethyl-2-butanol = shown in the F ball . stick labels Atom Atomic Weight amlatom Atoms Weight in compound mu atomc AmW atom atoms amu amWalom atoms aMu molecular weight of 2,3-dimethyl-2-butano...
1 answers
State the periodic law, and explain its relation to electron configuration. (Use Na and $\mathrm{K}$ in your explanation.)
State the periodic law, and explain its relation to electron configuration. (Use Na and $\mathrm{K}$ in your explanation.)...
5 answers
3TI Consider function f(z) where f"(x) = 2 (ln2)? + sin(a) Find f"(c) dz: b) Assume that f(0) = 1and f(2) = 1,find f(c)
3TI Consider function f(z) where f"(x) = 2 (ln2)? + sin( a) Find f"(c) dz: b) Assume that f(0) = 1and f(2) = 1,find f(c)...
5 answers
Question 1420 pts(20 points, 2 pts per correct answer) List out the ions that compose the following ionic compounds. The order of input for the ions is as follows: Atomic symbol then charge magnitude then sign, all without spaces or trying to use sub- or superscripts For example; the ion Ni2* would be entered Ni2+: lons with a charge magnitude of one (i.e. F ) can be entered as either F1- or F-_ Compounds Cation AnionSrFzCaSeRbzONisKBr
Question 14 20 pts (20 points, 2 pts per correct answer) List out the ions that compose the following ionic compounds. The order of input for the ions is as follows: Atomic symbol then charge magnitude then sign, all without spaces or trying to use sub- or superscripts For example; the ion Ni2* wou...
5 answers
Simplify the complex fractions.$$ rac{ rac{5}{2}+1}{ rac{3}{4}+ rac{1}{3}}$$
Simplify the complex fractions. $$\frac{\frac{5}{2}+1}{\frac{3}{4}+\frac{1}{3}}$$...
5 answers
Lel91(€)solution of (H): y" + p(c)y' + 9(c)y = 0 where and continous function OH an interval Assume that Yi(z) + 0 and setareJ plu) du 9i (t)92(r) = y1(z)(ignore constants of integration)
Lel 91(€) solution of (H): y" + p(c)y' + 9(c)y = 0 where and continous function OH an interval Assume that Yi(z) + 0 and set are J plu) du 9i (t) 92(r) = y1(z) (ignore constants of integration)...
5 answers
Problem 21.906 RoUre Lanuu CEI[Crinca cantma 6 0, Tm retoarlot COcieFe t15 ol cectC potra1] Wllearal cvarlng oleclk [tt ro norkenMrih honl 44t9t emnSntu'eliaaiZpI=neaAachanamanrinnunimValueUnitsSubitManueatnanelFene6m54r Kenelnetl44piddVeneeneneleppiepieio unitValueUnitsSubirauealAnatelZruvoy FetUbuciJutnl
Problem 21.9 06 Ro Ure Lanuu CEI[Crinca cantma 6 0, Tm retoarlot COcieFe t15 ol cectC potra1] Wllearal cvarlng oleclk [tt ro nork en Mrih honl 44t9t emnSntu 'eliaai ZpI= neaAach anamanrinnunim Value Units Subit Manueatnanel Fene 6m54r Kenelnetl 44pidd Veneenenel eppiepieio unit Value Units Subi...
5 answers
Which ion below is isoelectric with neon (Ne)? OA Li2+08.c2+ Oc0 0D. 02 OE N2-
Which ion below is isoelectric with neon (Ne)? OA Li2+ 08.c2+ Oc0 0D. 02 OE N2-...
5 answers
Find the current; through a resistor of resistance R = 4 Q if the voltage across the resistor is 8 V.A 60-Watt light bulb uses up (3600 s) .energy when left on for 1 hour
Find the current; through a resistor of resistance R = 4 Q if the voltage across the resistor is 8 V. A 60-Watt light bulb uses up (3600 s) . energy when left on for 1 hour...
5 answers
A plana E Jpon Iod Matekaur Kouth 200 Kin TAren chonges coune pexring of 1402 Hatck $0 E ur ulinour 4t? o EWum Itlc uimon In Lravel straight [utc, thc pilot knou > Llat she must Mnue lount lodh Hcu Iar plale frarn the sitpat" Raand , nince (uc decin71il ]a4m
A plana E Jpon Iod Matekaur Kouth 200 Kin TAren chonges coune pexring of 1402 Hatck $0 E ur ulinour 4t? o EWum Itlc uimon In Lravel straight [utc, thc pilot knou > Llat she must Mnue lount lodh Hcu Iar plale frarn the sitpat" Raand , nince (uc decin 7 1il ]a 4m...

-- 0.019349--