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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

**Chapter 7, Problem 6**

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**QUESTION:**

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.)

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### Questions & Answers

**QUESTION:**

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.)

**ANSWER:**

Step 1 of 2

It is given that,

.

And,

.

To prove that,

.