Given that a is a third-order matrix λ 100 λ 100 λ, find the cubic power of a, the first line λ 10, the second line 0 λ 1 and the third line 0 λ 1 First line λ 10 The second line 0 λ 1 The third line is 0 0 λ

Given that a is a third-order matrix λ 100 λ 100 λ, find the cubic power of a, the first line λ 10, the second line 0 λ 1 and the third line 0 λ 1 First line λ 10 The second line 0 λ 1 The third line is 0 0 λ

Let J =
┏0 1 0┓
┃0 0 1┃
┗0 0 0┛
Then J & # 178; =
┏0 0 1┓
┃0 0 0┃
┗0 0 0┛
J³=0
Original formula = λ e + J
﹙λE+J﹚³=λ³E+3λ²J+3λJ²+J³=
┏λ³ 3λ² 3λ┓
┃0 λ³ 3λ²┃
┗0 0 λ³ ┛
This j is useful in many places, especially in high-order
for example
﹙λE+J﹚^5=
┏λ^5 5λ^4 10λ³┓
┃0 λ^5 5λ^4┃
Γ 0 0 λ ^ 5 Γand so on