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.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 5EQ: In Exercises 1-12, determine whether T is a linear transformation. 5. T:Mnn→ ℝ defined by...
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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.
Transcribed Image Text: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.
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