do-the-three-lines-x_1-4-x_212-x_1-x_2-3-and-x_1-3-x_24-have-a-common-point-of-intersection-explain

Name: do the three lines x_1 4 x_212 x_1 x_2 3 and x_1 3 x_24 have a common point of intersection explain
Uploaded: 2019-09-05
Duration: 1 min 16 s
Channel: Numerade
Description: Do the three lines $x_{1}-4 x_{2}=1,2 x_{1}-x_{2}=-3,$ and $-x_{1}-3 x_{2}=4$ have a common point of intersection? Explain.

Question

Do the three lines $x_{1}-4 x_{2}=1,2 x_{1}-x_{2}=-3,$ and $-x_{1}-3 x_{2}=4$ have a common point of intersection? Explain.

Samantha Lincroft · Accepted 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.

Alina Krajewski · 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

Xiaomeng Zhang · Answer

So we got to you Crucial. Why? You tell Su minus street. So notice why you counts U minus floor blast Reax in denial Recreation Why you kills two to ax minus one. So here to fund the intersection were light miners for blast reax Eco&#x27;s to two AC minus one So how? Acsi coast to the street and every substituted acts in the equation My nose for last night when she comes to five So the car was here you call shoes 35

Xiaomeng Zhang · Answer

So here we light miners are half X Plus one equals +21 bulls axe last you, Then we can see my nose. So ah ah ha! Packs minus one. Forced actually goes two to minus while we&#x27;re have my nose street or four AC seacoast London ax here he calls to minors for Overstreet. And there we started Hugh Jackson. The crucial your how why you coast u minus her half times minus for over ST Class one. Done. We can see that Eco&#x27;s too to our street Last one. Reach Eco&#x27;s to five Overstreet. So the cardinals for a Jesse Coast to minus for over three five Overstreet.

Vipender Yadav · Answer

here we have to find the intersection of the two lines on the given two lines are X is equal to three on DDE. Why is equal to two X minus one? So let this real equation one on this mean equation too. Now we know not the values of X and y will be the point of intersection for the given two lines. So we know what had the value of X is three on. Now we&#x27;re plugging the value of X in the question to to find early off, away. So I&#x27;ll get two times off three minus one, which is equal to five. So the point of intersection for the given two lines is three. Come on, five. I hope you got the problem. Thank you.

Vipender Yadav · Answer

her. We have to find the intersection of the two lines on the two lines are explain why his equals 24 on DDE X minus Y is equal to 12. Now I&#x27;m going to art both the questions, So let this be. As for situation, this beer&#x27;s second equation so X plus Y is equal to four and x minus Y equals 2 12 So I&#x27;ll be adding both the equation to eliminate away. So we&#x27;ll get two weeks here on why end Viable. Cancel out on the hair will get 16 from her. The value of X comes out two years. Eight. Now we&#x27;re plugging the value off H in the equation one, so I&#x27;ll get eight. Bless. Why is equal to four from her Devil you off? Why is minus four? So the point of intersection for the given lines are h comma minus four. I hope you got the problem. Thank you.

Problem

Do the three planes $x_{1}+2 x_{2}+x_{3}=4, x_{2}…

Problem 17 Medium Difficulty

Do the three lines $x_{1}-4 x_{2}=1,2 x_{1}-x_{2}=-3,$ and $-x_{1}-3 x_{2}=4$ have a common point of intersection? Explain.

Answer

$x_{1}=-13 / 7$
$x_{2}=-5 / 7$
$(-13 / 7,-5 / 7)$

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

Linear Algebra and Its Applications

Catherine R.

Alayna H.

Caleb E.

Maria G.

Absolute Value - Example 1

Absolute Value - Example 2

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$x_{1}=-13 / 7$$x_{2}=-5 / 7$$(-13 / 7,-5 / 7)$

Linear Algebra and Its Applications

Catherine R.

Alayna H.

Caleb E.

Maria G.

Absolute Value - Example 1

Absolute Value - Example 2

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

Catherine R.

Alayna H.

Caleb E.

Maria G.

$x_{1}=-13 / 7$
$x_{2}=-5 / 7$
$(-13 / 7,-5 / 7)$

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

Linear Algebra and Its Applications