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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.

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

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 1

Systems of Linear Equations

Introduction to Matrices

Campbell University

Baylor University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

01:11

01:16

Do the three lines $x_{1}-…

01:42

Find the intersection of t…

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Three intersecting planes …

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02:37

Describe the set of all po…

03:11

Intersecting planes Find a…

01:22

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's try to solve the system of the first step Everton as this matrix right here. Now let'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's gonna give us you grow three off zero one negative one negative four. Now let'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'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't possible, so the system is inconsistent, meaning that it's does not have a solution set and therefore does not have a point of intersection

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