The concepts of Eigenvectors and Eigenspace center around vectors that, when a linear transformation is applied, only alter by a scalar factor. These vectors are not zeroes. The Eigenspace refers to the collection of all related eigenvectors for a specific eigenvalue, including the zero vector. To determine these, one must solve the characteristic equation, and then replace the eigenvalues in the matrix equation.
| Topic | Problem | Solution |
|---|---|---|
| None | If the column vector $\left[\begin{array}{c}5 \\ … | Solve the equation Av = λv, where v = \(\begin{bmatrix} 5 \\ -5 \end{bmatrix}\) and A = \(\begin{bm… |
| None | (a) Find two independent solutions of \[ \left\{\… | Given the system of equations: \[\left\{\begin{array}{l} \dot{x}=3 x+R y \\ \dot{y}=x+4 y \end{arra… |