Let \(\vec{x}\) be represented by the red arrow, and \(A\vec{x}\) by the grey arrow, for a \(2\times 2\) matrix \(A\text{.}\) Drag the tip of the red arrow to see the grey arrow change. Or drag the blue sliders to change the numerical values of the four entries of the \(2\times 2\) matrix \(A\text{.}\) You will not see the grey vector until you change the matrix using one of the two sliders on the left. Why is that? What are the eigenvectors of the initial matrix?
