if-the-equation-h-mathbfxmathbfc-is-inconsistent-for-some-mathbfc-in-mathbbrn-what-can-you-say-about

Name: if the equation h mathbfxmathbfc is inconsistent for some mathbfc in mathbbrn what can you say about
Uploaded: 2019-08-05
Duration: 2 min 22 s
Channel: Numerade
Description: If the equation $H \mathbf{x}=\mathbf{c}$ is inconsistent for some $\mathbf{c}$ in $\mathbb{R}^{n},$ what can you say about the equation $H \mathbf{x}=\mathbf{0} ?$ Why?

Question

If the equation $H \mathbf{x}=\mathbf{c}$ is inconsistent for some $\mathbf{c}$ in $\mathbb{R}^{n},$ what can you say about the equation $H \mathbf{x}=\mathbf{0} ?$ Why?

Runpeng Li · Accepted Answer

problem again. We need to apply the convertible metric spirit. So we know that each eggs equal see is inconsistent. So this isn&#x27;t inconsistent. Sorry. So this is inconsistent end. So this is actually the negation uh, r g? I&#x27;ll just write down here negation, uh, off part G. Uh, I am t Okay. So, equivalent in these seas, we have indication of I am t And we need to figure out the equation. It each acts because zero So in our you know where your burnable matrix theory room. We have part d r d. That is message. I just write down. Ready down again. Artie is equivalent to RG. So the litigation off party is equivalent to location off our G. That means Oh, what part D says if the question, actually zero has only the trivial solution. So indication off Part D. So that means what? What? What we can see about each axe equal zero, That is the system has nontrivial solution. Nontrivial solution. So that&#x27;s our conclusion.

Charles Carter · Answer

Okay, this problem has h of X equally X squared minus four x minus c and saying if we plug in C, it wants us to get see. So we&#x27;re gonna have C square minus four times, see? Minus seemed is equal to see. Okay. And so just wants us to pick a value that&#x27;s not zero. So if I If I, uh so we can reduce this to simplify this to C squared minus five C equals C and five seed of both sides will have C squared is equal to 60 and therefore C is equal to six. Okay, thank you very much.

Vicki Stebbins · Answer

Okay, Number 82. So question is, if I have f of X. Yeah, and it looks like this. Hey, someone x minus H 71 bodies. Where? What&#x27;s K then? I have G of X o. I and I had to ex non his age stepped in. U plus case of two. They couldn&#x27;t want it there. Okay. Should know. All right, this just means this is a second value. It&#x27;s nothing, you know, magical about it. Just a number two. You know that different. All right, so the question is, it says they have the same shape. Now, this is what tells me shape. Okay, It tells the shapes and it tells me direction. So if they have the same shape, that means that the A&#x27;s absolute value is the same. Okay, that gives me the same shape that one of them be positive in what could be negative. That gives me a direction, but that all they told me is that same shape that needs absolute value of a natural value. They are going to be signed because we could send shape. Can&#x27;t really tell you much about the h in the case, because this has to live with the horizontal placement in the case Have to do with vertical placement. And since they haven&#x27;t told you anything about the atria, Okay, You can&#x27;t making a determination that with that they had the same H values. OK, values, race. It&#x27;s about something you really determined there is that these were the same show that the absolute values that I wanted to the side

Alice . · Answer

Okay, So here is a problem that asked us to show why the equation X minus h squared plus y minus K squared is not wth e equation and is equal to minus four is not the equation for a circle. So we know that typically the equation of a circle is the one that falls bolos one, It&#x27;s right here. It&#x27;s the X minus. Each squared plus y minus. K squared is equal to R squared. So if we were to plug in the minus four into back into this ah form we get our squared is equal to minus four. And so the square root in order to find this are about you because the are in the equation stands for the radius of the circle would be the square root of minus four. And we know that we can&#x27;t take thescore irit of a negative number over the domain that we have of Ah oh, like whole numbers. We can only take the square root of, um, whole numbers so this radius doesn&#x27;t exist. If we were to give it a radius, it would be too. I excited the square negative for but however, since that radius doesn&#x27;t exist. Ah, therefore this circle also would not exist if we were to graft this. We can&#x27;t really graft to eye as the equation of the circle because it&#x27;s going to be so at some center h comma K and we can&#x27;t really go out a distance to eye. So therefore, the equation of this circle does not exist.

Mandeep Mangat · Answer

So here the question is Oh, explain why F X plus H minus X minus its age divided back to it should give a reasonable approximation off f Primex when f primex exist and h a small. So basically, I think this question is that proved that f crime X equal if explosion H minus f X minus age developer to which So let&#x27;s say we were h is very small. Is it a small distance? Let&#x27;s say this is a craft and this is some X value. And there&#x27;s another value off eggs at a distance. Very smaller distance H from here and on the Saito&#x27;s of the same distance from X. So let&#x27;s see. See that? Let&#x27;s say these are two points at a distance age from X, So if so, what&#x27;s the value of this X value? Here it will be ah X plus h Right. So the X plus age Same. Here&#x27;s how can find the stallion affects it will be x this X minus this value So this point would be six minus h. So if this is X minus age, the point that corresponds to this the vie value will be So. This is x minus h that I will be by value will be f X minus age. Same here. If this point is explicit age the vibe value Shay will be express age and if x plus teach So f primex means the slope derivative, which means we have to find the slope off the second line seek and Linus passing through these two points. So we have to find the slope off. This second slope is given by rise overrun. So here F Primex horizons by changing by the elusive I value. Here on the side is FX presage minus And this lies if x minus h and the denominator is changing X values of X value. Here is express age minus the first of this one x minus h. So rewrite the numerator and the bottom. If I open, the prince sees the sign will distribute negative sign so negative X plus h the sex cancels. So here we go. We were able to prove that this is a change in the sewage. So that&#x27;s what we were about. We&#x27;re supposed to prove their death. Primex is express H minus affects minus age. Derided by tours

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.

Problem

If an $n \times n$ matrix $K$ cannot be row reduc…

Problem 22 Medium Difficulty

If the equation $H \mathbf{x}=\mathbf{c}$ is inconsistent for some $\mathbf{c}$ in $\mathbb{R}^{n},$ what can you say about the equation $H \mathbf{x}=\mathbf{0} ?$ Why?

Answer

the equation $H x=0$ will not have the trivial solution only. It will have non - trivial solutions as well.

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

Linear Algebra and Its Applications

Heather Z.

Alayna H.

Caleb E.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

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the equation $H x=0$ will not have the trivial solution only. It will have non - trivial solutions as well.

Linear Algebra and Its Applications

Heather Z.

Alayna H.

Caleb E.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

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

Heather Z.

Alayna H.

Caleb E.

Kristen K.

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

Linear Algebra and Its Applications