Question

In problems 21 through 24, show that the matrix A is nilpotent and then use this fact to find the matrix exponential.

Answer 1

To determine if a matrix is nilpotent and find the matrix exponential

Step-by-step explanation:

To show that a matrix A is nilpotent, we need to find a positive integer k such that A^k = 0, where 0 is the zero matrix.

To find the matrix exponential, we can use the formula e^A = I + A + (A^2)/2! + (A^3)/3! + ... + (A^n)/n!, where I is the identity matrix.

For the given problems, you need to follow the steps to prove that A is nilpotent and then use the formula to find the matrix exponential.