(5) (2.2) (a) The set P = = {[ x1 - x2 2x1 x2+4x3 = 0 Xx3 =0} is a plane in R³. Find two vectors u₁, u2 € R³ so that span{u₁, u2} = P. Explain your answer. (b) Consider the three vectors u₁ = 2 3 -5 , նշ = 2 ' U3 8 Let b -5 = b₁ b₂ b3 be an arbitrary vector in R³. Use Gaussian elimination to determine which vectors b are in span{u₁, U2, U3}. Without further calculation, conclude that span{u₁, U2, u3} is a plane in R³ and identify an equation of the plane in the form ax₁ + bx2 + cx3 = 0.
(5) (2.2) (a) The set P = = {[ x1 - x2 2x1 x2+4x3 = 0 Xx3 =0} is a plane in R³. Find two vectors u₁, u2 € R³ so that span{u₁, u2} = P. Explain your answer. (b) Consider the three vectors u₁ = 2 3 -5 , նշ = 2 ' U3 8 Let b -5 = b₁ b₂ b3 be an arbitrary vector in R³. Use Gaussian elimination to determine which vectors b are in span{u₁, U2, U3}. Without further calculation, conclude that span{u₁, U2, u3} is a plane in R³ and identify an equation of the plane in the form ax₁ + bx2 + cx3 = 0.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 39RE
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If u use any type of chatgpt, will.downvote.
Transcribed Image Text:(5) (2.2)
(a) The set
P =
=
{[
x1
-
x2 2x1 x2+4x3 = 0
Xx3
=0}
is a plane in R³. Find two vectors u₁, u2 € R³ so that span{u₁, u2} = P.
Explain your answer.
(b) Consider the three vectors u₁ =
2
3
-5
, նշ =
2
'
U3
8
Let b
-5
=
b₁
b₂
b3
be an arbitrary vector in R³. Use Gaussian elimination to determine which
vectors b are in span{u₁, U2, U3}.
Without further calculation, conclude that span{u₁, U2, u3} is a plane in R³
and identify an equation of the plane in the form ax₁ + bx2 + cx3 = 0.
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