List of top Engineering Mathematics Questions on Determinants

Let

\[ M = \begin{bmatrix} 1 & 0 \\ 0 & 2 \end{bmatrix}, \quad K = \begin{bmatrix} 2 & -1 \\ -1 & 1 \end{bmatrix} \]

satisfy the eigenvalue problem:

\[ (M - \alpha K)\,\phi = 0 \]

The lowest eigenvalue \( \alpha \) is __________ (rounded off to two decimal places).

Let \( M = \begin{bmatrix} 1 & 0 \\ 0 & 2 \end{bmatrix} \) and \( K = \begin{bmatrix} 2 & -1 \\ -1 & 1 \end{bmatrix} \) satisfy the eigenvalue problem given by:
\[ (M - \alpha K)\phi = 0. \] The lowest eigenvalue \( \alpha \) is ________ (rounded off to two decimal places).