The eigenvalues of the matrix
are \( \lambda_1, \lambda_2, \lambda_3 \). The value of \( \lambda_1 \lambda_2 \lambda_3 ( \lambda_1 + \lambda_2 + \lambda_3 ) \) is:
Let \[ A = \begin{pmatrix} 1 & 0 & 1 \\ 0 & k & 0 \\ 3 & 0 & -1 \end{pmatrix}. \] If the eigenvalues of \( A \) are -2, 1, and 2, then the value of \( k \) is _.
(Answer in integer)
For the beam and loading shown in the figure, the second derivative of the deflection curve of the beam at the mid-point of AC is given by \( \frac{\alpha M_0}{8EI} \). The value of \( \alpha \) is ........ (rounded off to the nearest integer).
In levelling between two points A and B on the opposite banks of a river, the readings are taken by setting the instrument both at A and B, as shown in the table. If the RL of A is 150.000 m, the RL of B (in m) is ....... (rounded off to 3 decimal places).