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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,
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