Engg Mathematics P3

Choose the spectral radius of a matrix whose eigen values are -1, 2, -5

Find the eigenvalues of the matrix

Given that λ= 1 is a twice-repeated eigenvalue of the matrix, how many linearly independent eigenvectors correspond to this value of λ?

For an n × n real symmetric matrix it is always possible to find n eigenvectors e1, e2, . . . , en that are-

The 3 × 3 symmetric matrix A has eigenvalues 6, 3 and 2. The eigenvectors corresponding to the eigenvalues 6 and 3 are [1 1 2]^T and [1 1 −1]^T respectively. Find an eigenvector corresponding to the eigenvalue 2.