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## Homework Statement

Let A =

\begin{bmatrix}

\lambda & a \\

0 & \lambda \\

\end{bmatrix}

and B =

\begin{bmatrix}

\lambda & b \\

0 & \lambda \\

\end{bmatrix}

Assuming that a ≠ 0, and b ≠ 0 ; find a matrix X such that X

^{-1}AX = B.

## Homework Equations

(A- [itex]\lambda[/itex]I)v=0

## The Attempt at a Solution

I tried using the following logic: Let B = {v1, v2,....vn}

be the basis of F

^{n}consisting of the columns of X. We know that column j of B is

equal to [Avj ]B, that is, the coordinates of Avj with respect to the basis B.

But because of the two matrices having the exact same eigenvalues, I just end up with a=0, and am unable to actually find an invertible matrix X. Am I misreading the question, the logic, etc..?