(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

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

3. 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..?

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# Homework Help: Finding X of (X^-1)AX = B

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