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Linear Algebra: A Geometric Approach - 2 Edition - Chapter 7.1 - Problem 6
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Solutions for Linear Algebra: A Geometric Approach | 2nd Edition | ISBN: 9781429215213 | Authors: Ted Shifrin, Malcolm Adams 9781429215213

Solution for problem 6 Chapter 7.1

Prove that if p(t) = (t )3 and dim N(A I) = 1, then we must have N(A I) C(A I). (Hint

Linear Algebra: A Geometric Approach | 2nd Edition


Problem 6

Prove that if p(t) = (t )3 and dim N(A I) = 1, then we must have N(A I) C(A I). (Hint: If N(A I) C(A I) = {0}, use the twodimensional case already proved to deduce that dim N(A I) 2.)

Accepted Solution
Step-by-Step Solution:

Step 1 of 2

It is given that,

.

And,

.

To prove that,

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Chapter 7.1, Problem 6 is Solved

Step 2 of 2

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Prove that if p(t) = (t )3 and dim N(A I) = 1, then we must have N(A I) C(A I). (Hint