Let T ≤ L(V). Suppose T has the matrix representation with respect to a basis B = {V₁, ..., v6} for V given by [T] B = 2 12 [T]c= 12 (a) Find a basis C for V such that the matrix associated to T is 3 1 3 2 1 2 1 2 3 1 3 (b) What are the characteristic polynomial and minimal polynomial for T? (c) What are the eigenspaces and their dimensions?

Let T ≤ L(V). Suppose T has the matrix representation with respect to a basis B = {V₁, ..., v6} for V given by [T] B = 2 12 [T]c= 12 (a) Find a basis C for V such that the matrix associated to T is 3 1 3 2 1 2 1 2 3 1 3 (b) What are the characteristic polynomial and minimal polynomial for T? (c) What are the eigenspaces and their dimensions?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

100%

Let T ≤ L(V). Suppose T has the matrix representation with respect to a basis B =
{V₁,..., V6} for V given by
[T] B =
2
12
[T]c=
12
(a) Find a basis C for V such that the matrix associated to T is
3
1 3
2 1
2 1
2
3 1
3
(b) What are the characteristic polynomial and minimal polynomial for T?
(c) What are the eigenspaces and their dimensions?

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Step 1: Express T explicitly

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Step 2: Finding the characteristics and minimal polynomials

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Step 3: Finding eigenspace

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