[Linear Algebra] How do you prove this? Let {b1, b2, b3} be a basis for a vector space V . Let T : V → V be a linear transformation such thatT(b1) = b1,T(b2) = 2b1 + b2, and T(b3) = 3b1 + 2b2 + b3.%3|(a)Prove that T is invertible.(b)Find a formula for T – T-1.

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Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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[Linear Algebra] How do you prove this?

Let {b1, b2, b3} be a basis for a vector space V . Let T : V → V be a linear transformation such that
T(b1) = b1,T(b2) = 2b1 + b2, and T(b3) = 3b1 + 2b2 + b3.
%3|
(a)
Prove that T is invertible.
(b)
Find a formula for T – T-1.

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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