is it possible to solve (iv) without the dot product? 7. Let u, = (1,4,2), uz = (0,3,1), uz = (1,1,1), u̟ = (1,3, –3) represent fourpoints in the xyz-space, and S = {u1, u2, U3, U}.(i)in S.Show that we cannot find a plane that contains all the four pointsFind a linear system with 2 equations that represent two planes(i)U and V such that u; lies on U and u, lies on V, and u;, ug are solutionsof the system.(iiFind the equation of a plane P that contains three points in Ssuch that P is a subspace of R³.(iv)points in Rº such that the three points lie on a plane that corresponds toa subspace of Rº. Justify your answer.Write down a necessary and sufficient condition on any three

Please find the answer in the next step

Answered: iv) Write down a necessary and…

iv) Write down a necessary and sufficient condition on any three points in R° such that the three points lie on a plane that corresponds to a subspace of R'. Justify your answer.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.6: Rank Of A Matrix And Systems Of Linear Equations

Problem 68E: Show that the three points (x1,y1)(x2,y2) and (x3,y3) in the a plane are collinear if and only if...

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Question

is it possible to solve (iv) without the dot product?

7. Let u, = (1,4,2), uz = (0,3,1), uz = (1,1,1), u̟ = (1,3, –3) represent four
points in the xyz-space, and S = {u1, u2, U3, U}.
(i)
in S.
Show that we cannot find a plane that contains all the four points
Find a linear system with 2 equations that represent two planes
(i)
U and V such that u; lies on U and u, lies on V, and u;, ug are solutions
of the system.
(ii
Find the equation of a plane P that contains three points in S
such that P is a subspace of R³.
(iv)
points in Rº such that the three points lie on a plane that corresponds to
a subspace of Rº. Justify your answer.
Write down a necessary and sufficient condition on any three

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