Question

Write a brief note on Eigen Value and Eigen Vector. Find the eigonvalues and eigonvectors of the matrix:
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Answer 1

Step-by-step explanation:

Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed.

Answer 2

The eigenvectors v of this transformation satisfy Equation (1), and the values of λ for which the determinant of the matrix (A − λI) equals zero are the eigenvalues. Setting the characteristic polynomial equal to zero, it has roots at λ=1 and λ=3, which are the two eigenvalues of A.