# How to find a Matrix A from two eigenvalues and eigenvectors

I have a Eigenvalues -1 corresponding to eigenvector

And another Eigenvalue 2 corresponding to eigenvector

But they are asking for a Matrix A with these corresponding Eigenvalues and Eigenvectors My problem how do i find this Matrix i think i should use a Linear Combination of some sort but i don't know how??

• You have to know at least what the matrix's order has to be, otherwise it is completely hopeless to expect an answer to your question. Yet with the given data you already must know its order...BTW, your matrix can easily be diagonalized using those eigenvectors as basis... Aug 11 at 10:08

Suppose $$v_1, v_2$$ are vectors to the eigenvalues $$\lambda_1, \lambda_2$$, let $$S=(v_1,v_2)$$. Let $$A=diag(\lambda_1,\lambda_2)$$, you are looking for $$X$$ such that $$XS=SA$$, so you can take $$X=SAS^{-1}$$.