Let m(x) = minimal polynomial of A. A* = 0 and AM, then A satisfies x² = 0,k>n equation Minimal polynomial of A divides

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Let M X Minimal Polynomial Of A A 0 And Am Then A Satisfies X 0 K N Equation Minimal Polynomial Of A Divides 1 (85.15 KiB) Viewed 22 times

Kindly explain some of the lines, at least. Thank you. after putting in =>, the line was incomplete.

Let M X Minimal Polynomial Of A A 0 And Am Then A Satisfies X 0 K N Equation Minimal Polynomial Of A Divides 2 (24.92 KiB) Viewed 22 times

I have just attached the question too. 3.3 p4. Thank you.
Let m(x) = minimal polynomial of A. A* = 0 and AM, then A satisfies x² = 0,k>n equation Minimal polynomial of A divides any polynomial P(x) Where P(4)=0 m(x) tt ⇒ x² = q (x).m(x) deg m(x) ≤n Where ⇒m(x)=x² for Also, any matrix A satisfies its minimal polynomial. m(A)=0 Hence VI n
izable. What is the minimal polynomial of A? What can you say if A is tripotent (A³ = A)? What if Ak = A? 3.3.P4 If A € M₁ and Ak = 0 for some k > n, use properties of the minimal polynomial to explain why A" = 0 for some r ≤ n.