How to translate matrix from one side of an equation to the other?

44 Views Asked by At

I was wondering how to translate matrix from one side of an $=$ to the other and if the following was the right way to do it, that is to say add a transposed of the matrix on one side to cancel it and send the same transposed matrix to the other side of the equation:

\begin{align*} &V\begin{pmatrix}1\\-1\\1\end{pmatrix}=x\begin{pmatrix}1\\-1\\1\end{pmatrix}\\ &\Leftrightarrow V\begin{pmatrix}1\\-1\\1\end{pmatrix}\begin{pmatrix}1 & -1 &1\end{pmatrix} = x \end{align*}

Because in my casio 35 + calculator this creates a $3\times 3$ matrix whereas it should have been a single value as far as I am looking for eigen values.