Question

Are eigenvalues preserved by elimination? If so, provide justification. If not, provide an example of a matrix A whose echelon form U has different eigenvalues.

a) True
b) False

Answer 1

Eigenvalues are preserved by elimination in a matrix.

Step-by-step explanation:

True

Eigenvalues are preserved by elimination.

Let's consider a matrix A and its echelon form U. We know that A and U are similar matrices, which means they have the same eigenvalues.

So, the eigenvalues of A are preserved by elimination.