suppose-the-system-below-is-consistent-for-all-possible-values-of-f-and-g-what-can-you-say-about-the

Question

Suppose the system below is consistent for all possible values of $f$ and $g .$ What can you say about the coefficients $c$ and $d ?$ Justify your answer.
$$\begin{aligned} x_{1}+3 x_{2} &=f \ c x_{1}+d x_{2} &=g \end{aligned}$$

Samantha Lincroft · Accepted Answer

So in this problem, we&#x27;re told that this system is consistent for all values of F G and were asked what we can deduce about the values of C and D. And so what we&#x27;re going to do is look at this sort of left hand matrix here and take the determinant. And we know that for this to be consistent, the determinant can&#x27;t be zero. So remember that we do the determinant by doing kind of this curly fish pattern. So it will be one times d minus three times, see, and that we don&#x27;t want to be equal to zero in order for this to be consistent, which means that DE cannot equal three c.

Alina Krajewski · Answer

in this problem were given this system, and we&#x27;re told that it&#x27;s consistent for all values of F N g. I&#x27;ve gone ahead and written the system as this matrix right here, Um, in the Matrix, we know that A is gonna solve for X one. We&#x27;re told that a is non zero, But in order to get our answer for X one day is gonna have to be equal to one. To get a able to one, we can scale over one by one over a meaning we&#x27;re gonna multiply all of one row one by one of Ray, and that&#x27;s gonna give us a newer one off one be over a f over A and we&#x27;re still gonna have our original second room Now in our second road. We know that this D is gonna solve for X two and this sea is gonna have to equal zero. So let&#x27;s try equaling, see to zero and see the fact that that has on D until make c equal to zero. In this matrix, we can add negative. See time&#x27;s row one to row two. Um, that&#x27;s gonna give us a new row. Two of zero team minus C times be over a and Jean minus C times f over a. So Hugh have accomplished what we wanted Where this X one right here is equal to one. And here we have this equal to zero. Now we know that this variable here is gonna be your solution toa x two. And in order for the system to be consistence, this valley over here is gonna have to be non zero. So what we know about our values of A, B, C and D is that a d minus C times be over A cannot equal zero.

Vipender Yadav · Answer

her festival. We have to write the equation in standard form on Dhe. Then we have to Seoul equations also. So the given equations are two weeks as equals. Two minus three y plus four on the second equation is X plus y divided by three is equal to one now, other writing the equation one in a standard form. So we can write this equation as a two weeks plus three way. Is it quotes to four? I&#x27;ve added three y two both side of the equation. So I&#x27;ve got this result, which is a standard form of the equation on duh this equation gunrunners explosive. I as equals to tree. I&#x27;ve just multiplied both side of the equation by three. So I haven&#x27;t been this equation, which is standard form now. Are they multiplying this equation with minus two? So I&#x27;ll get minus two weeks minus two. Y equals two minus six on. Then we&#x27;re going to write the first equation. This equation below this will get two weeks plus three y is equal to four. Now, let&#x27;s art both the question when we&#x27;re goingto art the stoics on minus two weeks and the stewards we&#x27;ve cancelled out that is why multiplied this equation with minus two so that these dumb could be cancelled out here on hair will get minus sorry. Why three by mine issue is why on this is minus two, Sophia obtained a value of Maya&#x27;s minus two. Now will substitute value of eye in the equation to this equation. So I get X minus two is equal. The tree or ex comes out to be as five. So finally, we can conclude that the value of X is five on Valley off Y es minus two. So I hope you have initiative. Problem. Thank you.

Ankit Gupta · Answer

we have given a Y equals to the FX. Affects equals toe x Q x Q plus B X squared plus C explicit e. And now we have given that f off one equals toe minus for F minus one that is to f off two equals toe minus seven and F four minus two equals two minus F of minus two equals two minus 7.5 or two equals toe again minus seven. So boycott minus and no, we have to solve for the effects we have toe right, the value of ABC, Andy. So for this, we have to use metrics. So for this year I&#x27;m writing make This will be f one X equals to one. So this is a plus B plus C plus D equals minus four and second English in F minus one that didn&#x27;t minus one plus B minus C plus D equals two don&#x27;t. And now, if off to will give you here eight. This is cube eight. A bliss for would be plus two C plus d equals toe minus seven and also minus 80 and this one with a four B minus two c Bless B equals toe minus seven. So bigger these poor equation. And now the augmented might actually be here. I&#x27;m writing so 1111 and buy enough food. And here, minus 11 minus 11 And to he had eight float to one and minus Ilin and then minus 84 minus 21 and minus seven. So this is the augmented my life and no. So this is the moment in my drinks. And now we have to find a really off e b, c and D. And when we find the value off A, B, C and D, we get here equals two. Here this is one b equals so that it&#x27;s minus two Sequels to minus coat and e questo again one so that the value of A, B, C and e from solving this metric Forget ABC. So the question becomes here. The question is, why equals toe a X cubed plus B X squared plus c explosive, but the value of ABC Andy, we get here. Why equals toe affects equals toe. This is X squared minus two X squared minus four x plus one. So this is really

Vipender Yadav · Answer

hair. First of all, we have to write the given system off equation and standard form. And then we have the sold equation. So the given equations are three X plus y is equals to one on minus two weeks as equals two minus y bless too. No, this equation can minted in as three X plus three y is equal to one on this equation Gann murdered and as minus two weeks bless Why is equals to two? No, I&#x27;ll be multiplying this equation. Bye, minus three. So, first of all, let this be as equation One on this B s equation too. So when I multiplied the equation to with minus three, really get six times off X minus three way as equals. Two minus six on dhe. First equation right below it. So three X plus three y is equal to one. Now we&#x27;re going toe. Add about the equations so he&#x27;ll get Nynex on minus tree by and plus trioval canceled out. That is why we multiplied the equation to with minus tree so that it can be cancelled out here as equals to minus five. From here, the value of X comes out to be ours minus five, divided by night. No, I&#x27;ll be substituting the value off X in the equation. One you can subsidiary in equation to. Also it&#x27;s one in the same thing. You&#x27;ll get the same result so three times the minus faith by nine plus three times the Y is equal to one from hair will get minus five, divided by three Bless three way is equals to one or weaken right. Why is equals to one Bless five. Divide by three on dhe whole divide by three. So after simplification of will get why as eight. Divide by nine. So we have a plane, the value of X as minus five by nine on Really off. Why, as eight by night and now we have reject the result. Also for that really substituting the values in the equation. One you can subsidiary an equation to. Also it&#x27;s one in the same thing, so we get three. James off minus five by nine bless. Three times off. Aid by nine equals to one so heavily get minus five. Divided by three plus H, divided by three recalls to one Now will become binding the factions and I&#x27;ll get H minus five divided by three is recalled to one. Or we can say that one l equals to one hands. It can be concluded that the left side of the equation is you called the right side. So we can say that the values of X invited river plainness correct. I hope you got a problem. Thank you.

Vipender Yadav · Answer

heard this problem. We have to verify that a given function G or fix is the girls to see one it apart, minus two weeks. Bless C two times X to the power minus two weeks. Blessed to is the solution off the given differential equation, which is ju double prime mix. Bless four times geo fix plus four times G or fix hair. It is G prime mix so equals toe eight. Now calculate G prime mixed and little Georgie Primex under every plug The village in this equation to verify. So first of all, do Premix will be called studio differentiation of dysfunction. On that will be si 100 about minus two. X times minus two on now will use a productive room to find the differentiation of dysfunction. So see to you did about minus two weeks Bless. See to you do let me write this way X about minus two X times minus two So we can write this field. So no double Primex that will be equal. Stewart differentiation off do prime mix. So here will get minus two times minus two. See, even irritable minus two weeks. Or we can read this thing as four times. It&#x27;s one in the same thing. Bless the tradition of this function will be See to it about minus two X Times minus two. So we can right this way minus no. I&#x27;m digging a minus sign outside the bracket on I&#x27;ll be different hearing dysfunction so you get two games. See to times X Rated about minus two X times minus two. So it&#x27;ll become minus four. Bless. No. Two games. See to it about minus two weeks. So there&#x27;s a deficient that we&#x27;ve got always going to simplify. So we get four times. See one Interpol minus two weeks, minus two c. Tow it about minus two weeks on minus munitions places of four times. See to executed about minus two weeks on Dhere. We get minus two times. See to about minus two weeks. We&#x27;re going to combine like terms on these are the two like Tom&#x27;s. So the expression re gums four times. See, even you did about minus two weeks. Place I&#x27;m reading this stuff 1st 4 times. See two X times here the par minus two weeks minus four. See toe it about minus two weeks. So we have calculated both the dumps. It is by the depreciation that is deep remix and G double ceramics. Soul going to plug the values in this equation in this differential equation, So G double Prime X suitable Try mixes four times, See one it about minus Twix Bless four times C two times x You did the ball minus two weeks, minus four C to about minus two weeks. Bless four times G prime mix. So G premix is this So minus two times? See one needed about minus two weeks less C. Two about minus two weeks, minus two C. Two times Experian, about minus two weeks now Bless four times a G or fix said your fix of this. So see one upon minus two weeks. Bless. See to it about C two and there is excellent in their expiry about minus two X plus two. Now simply, we have to simply various expression, so that will be calls to four games and read to here four times. See one it about minus two weeks, plus four times. See two times X hearing about minus two weeks on minus four C. Two times you triple minus Truex Animal window multiplayer forbidden bracket. So you get minus eight times. See? Wanted about minus two weeks on bless four times. See to it about minus two weeks on here will get minus eight C two times Experian about minus two weeks. Now multiply four within the brackets will get full time. See one about minus two weeks, plus four times. See, do times. Experian about minus two weeks. Bless eight. Now will you do for the simplify So I&#x27;m going toe are the like terms. So if you observe carefully, these are the two legged ums. So we get four times. So the age thing. See what you did about minus two weeks in these two other light terms, so eight times C two times x unit about minus two weeks Onda This one as it is actually this term and this devil Cancer wrote so no need to write. Minus eight c one heard about minus two x minus eight C to expiry. The power minus two weeks on Bless eight. Now, again, these two terms will cancel out on these two does will cancel out. So we&#x27;re left with eight on which is equal to the right side. So finally be very fired. That the given function is equals to is the solution of the given differential equation. I hope you got the problem. Thank you.

Problem

Suppose $a, b, c,$ and $d$ are constants such tha…

Problem 27 Easy Difficulty

Suppose the system below is consistent for all possible values of $f$ and $g .$ What can you say about the coefficients $c$ and $d ?$ Justify your answer.
$$\begin{aligned} x_{1}+3 x_{2} &=f \\ c x_{1}+d x_{2} &=g \end{aligned}$$

Answer

$d \neq 3 c$

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David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications

Anna Marie V.

Alayna H.

Caleb E.

Michael J.

Absolute Value - Example 1

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$d \neq 3 c$

Linear Algebra and Its Applications

Anna Marie V.

Alayna H.

Caleb E.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

David C. Lay, Steven R. Lay, Judi J. McDonaldLinear Algebra and Its Applications

Anna Marie V.

Alayna H.

Caleb E.

Michael J.

David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications