b) For 7 in R", we say that is in the kernel of T if T(x) = 0. If x₁ and 2 are both in the kernel of T, show that ax + bx₂ is also in the kernel of T for all scalars a and b.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 31E
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b) For in R", we say that is in the kernel of Tif T(x) 0. If x₁ and 2 are both in the kernel of T, show
that ax₁ + bx2 is also in the kernel of T for all scalars a and b.
=
Transcribed Image Text:b) For in R", we say that is in the kernel of Tif T(x) 0. If x₁ and 2 are both in the kernel of T, show that ax₁ + bx2 is also in the kernel of T for all scalars a and b. =
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