# Proof involving eigenvalues and eigenvectors

Not what you're looking for? Search our solutions OR ask your own Custom question.

If x is an eigenvector of the nxn matrix A, prove that bx is also an eigenvector.

Â© BrainMass Inc. brainmass.com March 6, 2023, 1:14 pm ad1c9bdddfhttps://brainmass.com/math/linear-algebra/proof-involving-eigenvalues-eigenvectors-10047

#### Solution Preview

Since x is an eigenvector of the nxn matrix A, we know that Ax=lamda*x.

Now consider multiplying both left sides by the scalar b. This yields ...

#### Solution Summary

A step-by-step solution which shows that if x is an eigenvector of an nxn matrix, then bx is also an eigenvector. Word attachment included.

$2.49