Let A be a nxn matrix such that v1 and v2 are eigenvectors corresponding to eigenvalues lamba = 1 and lamba=3.

Question

show that v1 and v2 are linearly independent

Answer 1

Suppose c1 and c2 are constants such that

c1*v1 + c2*v2 = 0 (0 vector). To show: c1 = c2 = 0

Multiply both sides on the left by A and use Av1 = v1, Av2 = 3v2 to show that we must also have c1*v1 + 3c2*v2 = 0