Linear Algebra - Eigenvalues and Eigenvectors

Consider a vector p in 2-dimensional space. Let its direction (counter-clockwise angle with the positive x-axis) be θ. Let p be an eigenvector of a 2 × 2 matrix A with corresponding eigenvalue λ, λ > 0. If we denote the...

Consider the matrix A = $\begin{bmatrix} 50 & 70 \\ 70 & 80 \end{bmatrix}$ whose eigenvectors corresponding to eigenvalues $\lambda_1$ and $\lambda_2$ are $\mathbf{x}_1 = \begin{bmatrix} 70 \\ \lambda_1 - 50 \end{bmatrix...