Let β = [v1,v2,v3] be a basis for R3, where v1 = (1,0,1), v2 = (1,−2,0), v3 = (−1, 3, 1). Let T : R3 → R3 be a linear transformation. Compute: the standard matrix A for T if T(x,y,z) = (4y,x+2z,−2y+3z).

Let β = [v1,v2,v3] be a basis for R3, where v1 = (1,0,1), v2 = (1,−2,0), v3 = (−1, 3, 1). Let T : R3 → R3 be a linear transformation. Compute: the standard matrix A for T if T(x,y,z) = (4y,x+2z,−2y+3z).

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.CR: Review Exercises

Problem 18CR

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Linear Algebra - Isomorphism, Matrix of Linear Transformation

Let β = [v₁,v₂,v₃] be a basis for R³, where v₁ = (1,0,1), v₂ = (1,−2,0), v₃ = (−1, 3, 1). Let T : R³ → R³ be a linear transformation. Compute:

the standard matrix A for T if T(x,y,z) = (4y,x+2z,−2y+3z).

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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