do-the-three-planes-x_12-x_2x_34-x_2-x_31-and-x_13-x_20-have-at-least-one-common-point-of-intersecti

Name: do the three planes x_12 x_2x_34 x_2 x_31 and x_13 x_20 have at least one common point of intersecti
Uploaded: 2019-07-24
Duration: 1 min 40 s
Channel: Numerade
Description: Do the three planes $x_{1}+2 x_{2}+x_{3}=4, x_{2}-x_{3}=1,$ and $x_{1}+3 x_{2}=0$ have at least one common point of intersection? Explain.

Question

Do the three planes $x_{1}+2 x_{2}+x_{3}=4, x_{2}-x_{3}=1,$ and $x_{1}+3 x_{2}=0$ have at least one common point of intersection? Explain.

Alina Krajewski · Accepted Answer

this problem, Ask says, if he threw plane share. Point of Intersection, Point of Intersection is simply the solution set of a system. So let&#x27;s try to solve the system of the first step Everton as this matrix right here. Now let&#x27;s look at the first variable x one and attempts to get rid off the one x one and grow three right here. Do that. We can add negative one times over a one 203 and that&#x27;s gonna give us you grow three off zero one negative one negative four. Now let&#x27;s look at x two and try to get rid off the one x two in the third room. To do that, we can add negative one times you wrote to to row three, and that&#x27;s gonna give us a new row. Three of 000 negative. Five. What this new Row three is telling us is that for the solution toa have for the system to have a solution, zero must equal negative five. But this isn&#x27;t possible, so the system is inconsistent, meaning that it&#x27;s does not have a solution set and therefore does not have a point of intersection

Samantha Lincroft · Answer

and this problem. We&#x27;re given three lines and asked to see if they have a common point of intersection and if so, to find it. So the first thing that we&#x27;re going to do is write these lines in, make its form, and when we do, we get the Matrix written above, and once we have that, we&#x27;re going to use the one. Cancel out this too, and negative one and just see where that leaves us. And it turns out that when we do that, we actually have this matrix here, and it&#x27;s really noticeable that the second and third rose are basically opposites of each other&#x27;s. We have seven, the negative seven and negative 55 which means that by adding road to grow three well, actually, just get all zeros in that role when we can actually completely cancel out that row and therefore now we have essentially two equations anti variables. So we&#x27;re just gonna finish solving this matrix and so now will solve for so that the second variable they&#x27;re getting a 01 and also get the 10 in the top. So we get e identity matrix when once we have the identity matrix that will give us our final solution, which shows that these three lines do into sect. They intersect in the point, and the point is minus 18 over seven, minus five over seven.

Linh Vu · Answer

it was even Joe questioning the job plans of his plan is three X plus four y 8 31 The second plant. These explain why mine has is a coaching three. And now we need to send a system questions. Yeah, you know, just in front of us in question and with Tried to actually the X we get ego Julia three x 71 minutes For why, and it means that Thanks. God, you wanted the three on this farm. Three. Why? So we get the expression from the X now we wouldn&#x27;t you. The second question now and then we get one of the three minutes for under three wine. That&#x27;s why I&#x27;m honesty. You go to three. Doesn&#x27;t implies them. I say they were in co two, uh, one out of three minus three and we get nickel ju minus. I need under three and minus one out of three. Why? So I have expression for the Z. Therefore, we have the intersection with your plans. He stood up on the line now with the ex Echoed You wanted a three minutes for three wine. Why go to the Y in the ankle? Germany&#x27;s eight and three minus one of the three. Why it would have played this. Why you buy that? D Then again in the section becomes the ex in court. You wanted to three minutes Fund of three day. Why go today? And the Thinker humanist paid under three minutes One of the three the

Linh Vu · Answer

and, uh, a question that Jew plans. And first plan is three experts. Why Manistee include you to the 2nd 1 is to thanks months tree. Why? Plus is equal to minus one Now we need to serve the system. The question How did you find the intersection? Region It you plans when trick for this one would be. We would align now and we were at about and then we see for the extra get Nico to, uh five x for the one here getting Kojima minus two y And for these evil coaching zero Careful, cogent one here. And from here, we can express No. Ah, why would ankle too? Ah, minus one of a Jew. And then plus five out of two X now with expression funder. Why? They can pull it back to the first question You get a three x on then. Ah, minus 1/2. Plus Find out of your ex Manistee. Include you Ju on from here. We can find it in. Could you Ah, yeah. We would have joy to the other side and then we get English U minus five out of do three experts fight it. Your ex in the press a reverend are mature X So we get expression for disease. Well, therefore, we can we get the intersection becomes Don&#x27;t I know. So we have X We&#x27;re going to x y mwinkeljohn one minus one happens find Julie. Thanks. Z equals humanise fired a Jew Evident of two X Now every good replay this Thanks here and bind it D And then we have the question underline Good you d Why do you mind if I have plus 500 to day and the encouragement It&#x27;s 500 Juba&#x27;s 11 and a two day as well.

Linh Vu · Answer

three plans. That first plan is X plus two y two z. You go to three Mexican gonna experts to why personally say you got Unite. The last one is a doozy. Press for busy Nico to six and we need your services. The main question is near. Noticed that for the first and 2nd 1 If we do the subjection here, then we should get go to minus six. Z equals June the minus six. Therefore, we get dizzy and couldn&#x27;t you One will get is a good one. You can get here when we can cut you this six minus far tense Kwan, do we get a good to the Jew and when is equal to one why go to two We can find a thanks it will be can use this first question now So expect to get a three by minus two Why ministers e doing it included three minus Teoh attempts to minus June times one. Then we get me go to you being a minus six a minus three and the phone uh, intersection off three plans. One single point on despond is honest. Three. Why would you chew and see what you want

Linh Vu · Answer

you even that three plans. The first plan is the explicit trees A country? Why? Why class for Z Go to six then think Sleepless. Why six c. Banco Tonight you will need to sell the system in question is now there for the 1st 1? You can get an XP Koji that three months three z when the 2nd 1 can get in while in computer six months for the therefore quarter less When we put this job the X and the Y therefore Ghenda three Ministries E press six minutes for a Z plus six z fortune. I Yeah, we have these three here which arm honesty and it&#x27;s only culture and night It&#x27;s against the law And if we get minus ian coaches there are if all Z e coaches zero when Zika Jizo begin the thanks Every coach June the tree And why including six. Therefore we have only in the 603 La GI plans, uh, one single point and it&#x27;s fun to these 360

Problem

In Exercises $19-22$ , determine the value(s) of …

Problem 18 Easy Difficulty

Do the three planes $x_{1}+2 x_{2}+x_{3}=4, x_{2}-x_{3}=1,$ and $x_{1}+3 x_{2}=0$ have at least one common point of intersection? Explain.

Answer

The three planes do not have a common point of intersection.

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

Linear Algebra and Its Applications

Grace H.

Anna Marie V.

Caleb E.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

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The three planes do not have a common point of intersection.

Linear Algebra and Its Applications

Grace H.

Anna Marie V.

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

Grace H.

Anna Marie V.

Caleb E.

Kristen K.

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

Linear Algebra and Its Applications