Calculus Diagonalization

Question

Given that the matrix A has eigenvalues v₁=−8 with corresponding eigenvector v₁ = [1][2]

and v₂ with corresponding eigenvector v₂ = [2][3] find A

Answer 1

Consider applying one of the definitions of an eigenvalue.

A*V₁=-8V₁

A*V₂=eigen_value * V₂

As both V₁ and V₂ are column vectors with two entries, it follows that A must be a 2x2 matrix. A second eigenvalue was not provided, so the exact form of A cannot be determined.