this is a linear algebra question,on how to solve for a linear transformation. 1. Let L1 : R³ → R² be defined asL1(x) = L1 (x1, x2, X3)(0, x2 + x3).Is L1 a linear transformation? 2. Let L2 : R³ → R² be defined asL2(x) = L2 (x1, x2, 13) = (x1 +0.3x2, 13 + 2).Is L2 a linear transformation?

Answered: 1. Let L1 : R³3 → R² be defined as…

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1. Let L1 : R³3 → R² be defined as L1(x) = L1 (¤1, 02, X3) = (0, x2 + ¤3) . Is L1 a linear transformation?

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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Question

this is a linear algebra question,on how to solve for a linear transformation.

1. Let L1 : R³ → R² be defined as
L1(x) = L1 (x1, x2, X3)
(0, x2 + x3).
Is L1 a linear transformation?

2. Let L2 : R³ → R² be defined as
L2(x) = L2 (x1, x2, 13) = (x1 +0.3x2, 13 + 2).
Is L2 a linear transformation?

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.

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