Question

6&7

6. Many applications of matrices in both engineering and science utilize eigenvalues and, some- times, eigenvectors. Control theory, vibration analysis, electric circuits, advanced dynamics and quantum mechanics are just a few of the application areas. In a couple of sentences, give two specific examples of how eigenvalues/eigenvectors are used. You may use an informal search of the Internet. Find all values of a and b such that 1 b -2] L3] is an orthogonal set of vectors.

Answer 1

use of Ejen values & Essen Vections electric circuit & The eigenvachers of an eletre herwort are value of the boundary Voltage bon which the boundary voltage in a scalar multible of the boundary current.. The eigen values are voltages for which the network will behave in predictable way. Control system: The eigenvalues indicate the system stability of an eigenvalue has a positive real pant then the system is unstable - All eigen values should have negative read past so the system te Steeble. The eigen vectors help us find the controllability and observability of the systom, @ {[:][:].[!) im anthusmak is an onthogonal set of vecton Onthogonal Neetun means L2, B7-0 LC1231-1963)7 - 9+26+920 - 0 41-2).(963) > 0 49 +6 - - - eh ② x 2 – en o

79 -리2 = - ] so by echo 3426490