Answered: Let (e₁,e2, es} be the standard basis…

Let (e₁,e2, es} be the standard basis of R³. If T: R³ R³ is a linear transformation such that 4 ---E T(e₂) = 2 , and T(es) = 2 T(e₁)= then T( 0 EL-BI )= -2 4

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 5CM: Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).

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Linear algebra q5

Let {e₁,e2, es} be the standard basis of R³. If T: R³ R³ is a linear transformation such that
4
---E
‚T(e₂) =
2
, and T(es) =
2
T(e₁)=
then T(
0
E-BI
)=
-2

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

Expert Solution

Step 1

$Given that Let \{e_{1}, e_{2}, e_{3}\} be the standard basis of R^{3} . Let T : R^{3} \to R^{3} is a linear transformation such that T (e_{1}) = [\begin{matrix} 0 \\ - 4 \\ 3 \end{matrix}], T (e_{2}) = [\begin{matrix} 4 \\ 2 \\ 2 \end{matrix}], T (e_{3}) = [\begin{matrix} - 4 \\ - 1 \\ 4 \end{matrix}] .$

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