Algebra dedr3: Obliczyć Aⁿ i Bⁿ dla dowolnego n ∈ N, jeśli: A = 4 1 0 0 4 1 0 0 4 B= 9 1 0 0 9 0 0 0 4

jc: A=4+C C= 0 1 0 0 0 1 0 0 0 C²= 0 0 1 0 0 0 0 0 0 C³ = 0

	n 0		n 1		n 2
An = (4+C)n =		4n +		4n−1C +		4n−2C2 =

4ⁿ n4ⁿ⁻¹ 2n(n−1)4ⁿ⁻³ 0 4ⁿ n4ⁿ⁻¹ 0 0 4ⁿ