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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.

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.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
Problem 53EQ
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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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