If A=pmatrix-100pmatrix, B=pmatrix+100pmatrix are two (column) matrices, then AB^T is a no…

Question

If $A=\begin{pmatrix}\alpha-1\0\0\end{pmatrix}$, $B=\begin{pmatrix}\alpha+1\0\0\end{pmatrix}$ are two (column) matrices, then $AB^T$ is a non-zero matrix for $|\alpha|$ not equal to

Accepted Answer

$AB^T=\begin{pmatrix}\alpha-1\0\0\end{pmatrix}\begin{pmatrix}\alpha+1&0&0\end{pmatrix}=\begin{pmatrix}\alpha^2-1&0&0\0&0&0\0&0&0\end{pmatrix}$.

This is non-zero exactly when $\alpha^2-1
e0$, i.e. $|\alpha|
e1$.

Solutions · 1