let-l-be-the-line-in-mathbbr2-through-the-points-leftbeginarrayl1-4endarrayright-and-leftbeginarrayl

Question

Let $L$ be the line in $\mathbb{R}^{2}$ through the points $\left[\begin{array}{l}{1} \ {4}\end{array}ight]$ and $\left[\begin{array}{l}{-2} \ {-1}\end{array}ight]$ Find a linear functional $f$ and a real number $d$ such that $L=[f : d] .$

James Chok · Accepted Answer

okay. In this question, we want to find the l line l that prostitutes pimps be wanting to be true. The pistol rule. Find door translated like I don&#x27;t know which positive. Very be to be one. Performing calculations minus two minus one, which is minus three minus one minus four is just minus five. So the point is, in albums, it must be perfectly clear to this line out here. So if you spend a nickel in the Bumble Bee to mind what our victim, this should give you so in one. And Chief Well, I thought that was minus three and Mars by which is even too negative. Three and one and two. Today&#x27;s long for anyone. We just have this need to name two live and chewed over. So then we just choose a model for into cancer satisfaction. So this is choose end to minus three at an and one is equal cheered. So then you have and it&#x27;s even true. Five and wise three. So then we&#x27;re functioned x one x two is even to you and X, which is to be five x one minus three x tooth to this function. Come dysfunction represents all lines with which is parallel to this. Inspected by open ridiculous Inspector. Right here. So to get back online, Ellis on what we need to do except servitude. One of these points in anticipation. So we can either pull minus two miles. One no one in for closer this case. It was wonderful. A 14 executive flats, as one wishes you find minus three times What was she 12. This is my son Thio Online l is along. L is Why x one? Twice three x two 97 Oh, by x one one&#x27;s three x to just seven is equal to zero.

Julie Silva · Answer

So in this problem, we want to find the values for and then be where f of zero is to an f of two is equal to negative four. And then we&#x27;re gonna write an expression for the linear function off of s. While our hint here is to write our to function values as ordered pairs. Well, remember, inside our preface eases our X value and what it&#x27;s equal to is our Y value. So f of zero equaling two means we have the order pair zero to and when f of two is equal to negative four. We know that we have the order paired to negative four, and these two points must fall on the same line. So we&#x27;re gonna go ahead and find a slope. To do this. We&#x27;re gonna use our cell formula. Why Sub two minus y sub one divided by X of two minus x aboard. So I&#x27;m gonna leave with my ordered pairs. Let&#x27;s start with the first order pair. So zero will be except one two will be vice of one from the second order pair. She will be, except to and negative four will be y subdue. So let&#x27;s substitute in our values. So we&#x27;re gonna have a negative for minus two. Divided by two minus zero. Well, negative four minus two is negative. Six and to minus zero is too. And negative. Six divided by two is negative. Three Perfect. With now found m m is negative. Three now, remember, be represents our Y intercept. Let&#x27;s take a look at this point because x zero. That means this is our Y intercept, which tells us that B is equal to two. So now we&#x27;ve solved for M and B. Now we can go back and rewrite our function so we&#x27;ll have f of s is equal to m, which was negative. Three so of negative three us plus beef which is to so our lanier function will be f of s equals negative three us.

James Chok · Answer

okay in this question, over need to do is on the maximum value F at P. One p to p three. So if you value weighed at P one is equal to zero plus minus, one gives you a modest one if you bother what it at peak, too, is equal to two plus one. Gives you three. F evaluated at p three is equal to one prostitute, which gives you three. So the maximum values is three given at the points he won and p two. For this question, we go f at P one. Is it 20 minus minus? One gives you one. If that&#x27;s pee, too, is equal to minus one. Gives you one. And if at p three, if you could choose one minus two, which is modest one seven, the maximum value is given by is one at the points p one and P two off with last one F at P one is equal to monetary times. You&#x27;re zero last one, if that&#x27;s pee, too. Music minus two times like two miles. Four plus one miles. Three F at P three is equal to minus two times one gives you minds. Two plus two gives you zero, so the maximum value is zero given at points a three

Vishal Parmar · Answer

great to find the value effort to substitute to forex. So you&#x27;re F minus two. That is a good of duty. Ready by to bless for two plus four that is equal to six and two by six. That is sick. Or do one by three. That is the value off F off to now. Substitute minus three Forex. But your duty reading by my history. Class four No. Four Ministry that is equal to one and two divided by one type is a widow do but your f off my nasty. That is equal to now. Substitute. Okay, Forex of your Fok Statistical Do do the right Gave less. For what did you dance? Square minus one or X? You&#x27;re doing the rated by K squared minus one and blast forties Allergies. Now you&#x27;re four minus one. That is equal. Do three. That is the real Your gay square, minus one. Thank you

Carson Merrill · Answer

so going along with the hand, we&#x27;re going to let f of acts equal a X plus b Um then, since we know f of A plus B equals F plus f B, we&#x27;re going to write F of a plus B that&#x27;s going to equal a times a plus B plus B, which will equal a times little A plus a times B plus B. And now we can ah also see that f of A plus f b equals a big a little A plus B plus big a little B plus B. Now we know that these two are equal to each other so we can set these two equal to each other. We have a big a little a big a little B B people big, a little a but the but they a little b the bees. Two of these bees will cancel. I am and will get these canceling, which tells us that B equals zero. So if we go back to our original function, f of X equals X plus B, we see that it&#x27;s just a X because B is equal to zero, and this is a linear function that will pass through the origin

Zach Wiebe · Answer

All right, So this is a tractor to section four. Problem number 19 Um, And for this one, our task is to graphic function with some restrictions. So first off, um, if our function is f of X, half of two has two equal five. The first derivative of the function at two is 1/2 in the second derivative of the function. It too zero. So if we start, we can put are to mark somewhere around there, which means our five mark would probably be about there. So here, this just means that the point two comma five is on the graph. And if that&#x27;s the case, then that will satisfy Heartwood. So we can put the point to common five right there. And our first condition there is satisfied. For the 2nd 1 We have a prime of two equals 1/2. And this just means that the slope at this point that we&#x27;ve put out has to be 1/2 So that might look if we draw the slope on there, it could look something like that. Um, and that&#x27;s just arc Tangent line. That&#x27;s not what the actual graph is gonna look like. It&#x27;s sort of gonna act as a guideline for this last one. We can go ahead and check that off since the derivative there since our tangent line there as a slope of 1/2. Now, if you look at this last condition, F double prime of two has to be positive. This just means that the second derivative is positive. It too, which means it&#x27;s curving up and that the slope is increasing. Um says since the slope is increasing, it means we have this point with a slope of 1/2. And that means from there we go on the slope has to be has to continue to increase after that, um so that could be drawn as something like that. Something along those lines. And this works because it is a function. It&#x27;s continuous, and there&#x27;s no two y values for every X value. Um, it has a point at two comma five. It&#x27;s a tinge of line right here as a slope of 1/2 and it is Khan gave up. Its in the second derivative is positive. So this function right year fits our requirements, and that is one possible solution to these

Problem

In Exercises 3 and $4,$ determine whether each se…

Problem 2 Medium Difficulty

Let $L$ be the line in $\mathbb{R}^{2}$ through the points $\left[\begin{array}{l}{1} \\ {4}\end{array}\right]$ and $\left[\begin{array}{l}{-2} \\ {-1}\end{array}\right]$ Find a linear functional $f$ and a real number $d$ such that $L=[f : d] .$

Answer

$Q(y)=7 y_{1}^{2}+4 y_{2}^{2}$

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

Linear Algebra and Its Applications

Catherine R.

Heather Z.

Kayleah T.

Joseph L.

Vectors Intro

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$Q(y)=7 y_{1}^{2}+4 y_{2}^{2}$

Linear Algebra and Its Applications

Catherine R.

Heather Z.

Kayleah T.

Joseph L.

Vectors Intro

Vector Basics - Example 1

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

Catherine R.

Heather Z.

Kayleah T.

Joseph L.

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

Linear Algebra and Its Applications