what-vector-in-mathbbr3-has-homogeneous-coordinates-leftfrac12-frac14-frac18-frac124right

Name: what vector in mathbbr3 has homogeneous coordinates leftfrac12 frac14 frac18 frac124right
Uploaded: 2020-07-13
Duration: 1 min 26 s
Channel: Numerade
Description: What vector in $\mathbb{R}^{3}$ has homogeneous coordinates $\left(\frac{1}{2},-\frac{1}{4}, \frac{1}{8}, \frac{1}{24}\right) ?$

Question

What vector in $\mathbb{R}^{3}$ has homogeneous coordinates $\left(\frac{1}{2},-\frac{1}{4}, \frac{1}{8}, \frac{1}{24}\right) ?$

Ankit Gupta · Accepted Answer

we have our victim required minus zero comma minus it. I need to explain a unique like which has the same direction. So really no required actor. And by tradition, this is required are 30 right? No need to go. First of all, the new guys break trying to get this a week ago. Minus goodness minus beats. This comes out of the square who got We can simplify this as still swim archetype by 70 that this becomes no one required. Maybe divided by born. That is my industry were divided by 270 coma minus divided by Do you write this as my this line divided by you&#x27;re 70 mines?

Thomas Pauly · Answer

this problem gives us a vector value function and were asked to extract or find the Parametric equations. Okay, so we have our teasing three t square times. I had minus two J hat. Really? What we want to find except e. And why of tea. So we know that the general form for this vector valley function is gonna look like this two dimensions. It&#x27;ll be exit e times I had plus live t I was j had he&#x27;s gonna match these. So this is what&#x27;s in front of the I had so x 30 years equals three t squared in. This is what&#x27;s a front in of the J hat. So no. So that&#x27;s too. But really, it&#x27;s negative too. So why of tea is just negative, too, So it&#x27;s actually free of tea, but we still call it a Parametric equation and say it&#x27;s a function of t were given a vector value function. We found the Parametric equations from it

Micah Hurewitz · Answer

So for this question, we have B complex number 1/2 plus 3/4 I So, for this complex number we are finding are so let&#x27;s take a look at the complex plane. We have 1/2 in the rials. So this is the rials and in the imaginary is we have 3/4. So our point will be right here and are will be this vector. Well, we don&#x27;t have numbers that are super easy to work with in terms of Pythagorean triples. So we&#x27;re just going to plug these numbers into our formula where we have r equals the square of a squared plus B squared. And for this question, we have the square of 1/2 squared with this in parentheses, plus 3/4 squared. So three fourth squared. So let&#x27;s jump down here, and this equals the square of 1/4 plus nine 16th. Now, if we want to have a common denominator, the 1/4 we can write as for 16th so then we have the square of 13 over 16 and we can leave this all in the radical or we can take the square root of 16 out and write as the square of 13 over. Yeah, but this is going to be our answer. So this is or for the complex number 1/2 plus 3/4 I

Donald Albin · Answer

Okay. Um, I already showed most of the work for this problem. Um, the question is determined whether the given vector set, which is up here, spans riel two dimensional space. So the first thing we can do is we can draw the three vectors, so V one is drawn and red down here. Right here. Um, six common negative, too. V two is drawn in green right here, negative to common 2/3. And V three is drawn, and blue down here noticed that all three vectors our co linear. And we know that if all three vectors air Colin ear that it&#x27;s not going to span um, the vector space on page 275 there&#x27;s an informal statement that any to non zero and non ca linear vectors, we&#x27;ll spend two dimensional real space. But we don&#x27;t have to know non cool in your vectors. These are all co linear. So now we convey again a more formal analysis. I wrote down three vectors and then I wrote down that the vectors defined his x one x two. Any vector x one x two can be written as a combination of the three vectors. A constant times the first vector plus the constant times The second vector plus a constant times the third vector. So down here I wrote the three vectors. The first vector is six common negative too. The second vector is negative two comma 2/3 And the third vector is three common negative one. If you ik wait only the x coordinates. You get this equation If you equate only the ah, why coordinates or, in this case, the X two coordinates You get this letting see one equal are any constant are And you know what? I&#x27;m going to let No, I&#x27;m gonna let that go. Then we can write this again, but instead of C one I&#x27;m rating are in its place. So six R minus two C two plus three c three is x one. And, um, the 2nd 1 is also is x two. What a day did then is wrote it in matrix form so we can take the, um court. The coefficient in front of C two immigrated here Coefficient in front of C three Rated here coefficient coefficient Time seat C two, c three x one minus six are So I just subtracted this six are from both sides and and added, The two are to both sides of the second equation. So then I wrote a determinant of the first the a matrix, and I find that that determinant equals zero. And that means that this system does not have a solution because that matrix is not in vertebral then, for ah x one x two in riel space. The system does not have a solution. And so again, even with the more formal analysis, the answer is no. Um, the set of vectors does not span riel two dimensional space.

Lu He · Answer

So if we want to buy the major city by dimensions there have sent if asked the one on December who we need to make sure the lost Borio upto chess move after transformations that also you can be job I mean, up before and after the transformation that values should be the Seine. Okay, so it s set a new majors called B and B Ys one you know, you know, one person by look Sorry. You should be one point who if I one year old one you know, you know? So this maitresse meant it tries the boy as why you it&#x27;s get the new majors after transformations and the better should be as prospect 1% and five I And why? And yet so you can see that the last world does not trench. Ah, that means the yet are you can be dropped. So if we drop the yet borough, we get the san transformation as the eight times ah s five better. So if we drop the yet you get this them I&#x27;m so after. Ah, a major is I mean, the measures in assemble one ties That&#x27;s why better So the answer we get it should be bay me is

Problem

Are $(1,-2,3,4)$ and $(10,-20,30,40)$ homogeneous…

Problem 15 Easy Difficulty

What vector in $\mathbb{R}^{3}$ has homogeneous coordinates $\left(\frac{1}{2},-\frac{1}{4}, \frac{1}{8}, \frac{1}{24}\right) ?$

Answer

$(12,-6,-3)$

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

Linear Algebra and Its Applications

Grace H.

Heather Z.

Alayna H.

Caleb E.

Absolute Value - Example 1

Absolute Value - Example 2

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$(12,-6,-3)$

Linear Algebra and Its Applications

Grace H.

Heather Z.

Alayna H.

Caleb E.

Absolute Value - Example 1

Absolute Value - Example 2

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

Grace H.

Heather Z.

Alayna H.

Caleb E.

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

Linear Algebra and Its Applications