\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Consider the matrix \(\mathbf{A} = \begin{pmatrix} 1 & 1 \\ 4 & 1 \end{pmatrix}\) and the vector \(\mathbf{x} = \begin{pmatrix} 1 \\ 2 \end{pmatrix}\).
  1. Calculate the product \(\mathbf{A}\mathbf{x}\).
  2. Hence, determine the eigenvalue \(\lambda\) associated with the eigenvector \(\mathbf{x}\).

Capture an image of your work. AI teacher feedback takes approximately 10 seconds.