find-an-equation-involving-g-h-and-k-that-makes-this-augmented-matrix-correspond-to-a-consistent-sys

Question

Find an equation involving $g, h,$ and $k$ that makes this augmented matrix correspond to a consistent system:
$$
\left[\begin{array}{rrrr}{1} & {-4} & {7} & {g} \ {0} & {3} & {-5} & {h} \ {-2} & {5} & {-9} & {k}\end{array}ight]
$$

Samantha Lincroft · Accepted Answer

So for this problem were asked to find the values of G, H and K that will make this system consistent. And to do that, we&#x27;re going to start by trying to put the system in triangular form. So first we&#x27;ll get rid of that negative, too. And we&#x27;re keeping track of what&#x27;s happening to the variables on the right. You So that gives us a K plus two g in that bottom, right? And so now we&#x27;re going to try to get rid of that. Ah, 13. But we&#x27;ll know this, actually, that we have this minus 55 And so, actually, what happens is if we have these two equations together, just as they are, we end up with zeros in the bottom, and we have actually no one here or no way Thio go about getting a triangular form here. And because of that, it means that the only way that we&#x27;re going to be able to actually say that this equation is consistent is if this bit here h plus que plus two g turns out working out to zero, in which case we&#x27;ll be able to create something consistent from the top to Rose and So the solution to our problem is that in order to create a consistent matrix here, we&#x27;re going to need HBO&#x27;s Capel&#x27;s to G to be zero.

Sungkyung Lee · Answer

this problem is asking us to set of metrics. Equation from system equations were given to system of equations. One is too g plus three eight as you could to eight. And the other equation, it will be four. Mine, us G. Negative seven. Wait, you go, too. Negative fight. So how do we set a Metrix equation to settle metric The question we need the formula. It is. Hey, X is equal to be. We&#x27;re at a where a is coefficient metrics. Thanks is variable matrix and B is constant metrics. So if he set up that in the tricks from it&#x27;s gonna be so Let&#x27;s put quickly symmetry for, uh, queen. So Okay, So before we said it all, let&#x27;s find the variable first. So we have two variables and two equations, right? G is gonna be our first variable, and eight is gonna be our second variable, and it&#x27;s coefficient goes to a so we can say to plus three, we don&#x27;t put plus here because it&#x27;s in metric from then we put negative for maybe put negative placement. Negative seven. No, these are our quite efficient A and we put very evil. Since we have two variables that you&#x27;re G eight key. And normally we put, um, vertical. We don&#x27;t put it horizontally. There is a call to be is just constant. They&#x27;re not coefficient. Oh, um very variable. Very ables. They were going to be just constant means, just numbers. Ls there gonna be a then negative fight? So this is our X is gonna be our variable, which is richer, G n h and B. Is there a koi fish? I mean, constant. So a negative.

Ankit Gupta · Answer

in this caution we have given here. Or when did my tricks and such as three minus quite one. Good. And also the constant, um, one minus two. Okay, so we have to convert them in a question form. So as we know, that augmented my tricks consisted Awful. Oh, very Bill coefficients and as well as constant. Um, so this type of matrix contains the completion dog food that even such a X and vice with this movie is three eggs minus five. Why is it Quito? And it will be equal to the concern towns that this one similarly next equation in previous X plus four by is a quarto minus two. So these other questions also this fomented metrics, okay?

Charles Carter · Answer

he said for this prom money to set up our matrix of coefficients for these linear equations referred Super 29 we&#x27;re gonna have negative five and seven and then two and negative three. So a in bursts. Let&#x27;s just put this in the calculator to get the the inverse matrix serpent in negative five and seven. I&#x27;m two and negative three. It&#x27;s the inverse matrix is gonna be negative Three negative seven and negative to negative five. Case of her part A We&#x27;re gonna take the inverse matrix and multiplied by r k matrix Super Part a r k matrix is gonna be negative five Positive one We we multiply that that&#x27;s gonna give us our excellent X two values and multiple on those major cities will give us the values Uh, for X one, we&#x27;re gonna have eight for X two. We&#x27;re gonna have five okay for part B, we&#x27;re changing this K values to be a negative four. So you multiply that by a inverse, it&#x27;s gonna change our accident. XT I is such as change about bee matrix right now based on the X one and X two, values will be equal to four okay and then part C. We have K one is equal to six and K to Z equals zero and said multiplying those it&#x27;s going to give us a value of X one is equal to negative 18 and X two is gonna be able to negative 12 day. Thank you very much.

Ankit Gupta · Answer

as we have given here and open Did my place minus one minus two 304 tu minus 10 Also, it contains the constant term as six to nine. Okay, s. So we have here augmented my tricks of which contains. So I only know the completion so valuable and also the constant. Um so let&#x27;s say the completion variables are x rays it, so the equations will be else here minus eggs minus two. White Bless three Said is accorded the Constant Artist. Six similar living extra question would be as as a coefficient of X zeal. So they this equation NVs pool, right as they is, he quietly do on the next aggression of years two x minus, right Plus, also even be called zero as coefficient of that zero here and the constant on this night. So these are the equations off this giving off? When did my tricks here? Okay,

Ankit Gupta · Answer

given increase in PSA Pleas E blessed Dukie. You will do it. And second question is minus seven, gate 80. And since we have to solve this using inverse matter it forming, so we&#x27;ll first right this into metric formers coefficient of Jenkins. And we&#x27;re gonna three for one do and minus seven on Jan. Gig and reorganise. They just seemed alien writer. Well, like the metrics on late. Now, let&#x27;s suppose this is B. This is X and really cool. It&#x27;ll be So here. You late. Ex surgical toe meaningless. Hey, I know the value off. In worst, we can cancel it if we knew that. Each vehicle and me see Andy then in one is equal to one point a B minus. Lucy and metrics be e minus B and minus state. So you didn&#x27;t this concept there? We have a s. Tony do one minus seven. So begin late in losses One of one into minus seven, minus one. My big black dick. They relate Minus seven, then here to the and then minus two and minus one. So in one is coming as one. Be weighted by minus than mine used to. This is minus seven minus two minus one. The so here in the middle of the night. One day later, the mind splendidly and minus seven minus two, minus one in three. This is about being list. Now we have to find the value off Ex. Too late exist, Jacob. Monty Mack tricks so we can write a J Comma K is acquittal minus one by 20. In place of any worse, we&#x27;re dating minus seven minus two minus one. And see multiplayer. Let&#x27;s be millions. Do it at 80 in metrics. So this is equal minus one by 20 then minus seven. My deployed with it minus two. Motive leg rickety, minus one will be played with it than plus three months of lying with Katie. So if we calculate this and their daddy next time, we can light it. Minus one by 20 and eating 27 minus of physics. And Linus, 26 minus eight left, 54. So here we can wait minus one by 23. And yet my ears too. 92 we&#x27;re going to say Kerrigan 8 54 minus eat 46. So it will send this minus 23 inside. This will be minus 92 a born minus 23 and 46 Evelyn Quantity. So here we have day coma. You and Gae In Matrix with tonight s this is look. And it looked minus ST very late, minus two. So we can see that Jay Z look and gazing minus two. So does we can conclude. Here s does the value off day is full and okay is minus two.

Problem

Construct three different augmented matrices for …

Problem 25 Hard Difficulty

Find an equation involving $g, h,$ and $k$ that makes this augmented matrix correspond to a consistent system:
$$
\left[\begin{array}{rrrr}{1} & {-4} & {7} & {g} \\ {0} & {3} & {-5} & {h} \\ {-2} & {5} & {-9} & {k}\end{array}\right]
$$

Answer

The system is consistent if $2 g+h+k=0$

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

Linear Algebra and Its Applications

Catherine R.

Heather Z.

Alayna H.

Kayleah T.

Absolute Value - Example 1

Absolute Value - Example 2

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The system is consistent if $2 g+h+k=0$

Linear Algebra and Its Applications

Catherine R.

Heather Z.

Alayna H.

Kayleah T.

Absolute Value - Example 1

Absolute Value - Example 2

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

Catherine R.

Heather Z.

Alayna H.

Kayleah T.

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

Linear Algebra and Its Applications