Reference no: EM131008399
1. The goal of this problem is to find the eigenvalues and eigenvectors for the following matrix:
(a) Find the eigenvalues of B.
(b) Find an eigenvector v1 corresponding to one of the eigenvalues.
(c) Find an eigenvector v3 corresponding to the remaining eigenvalue.
(d) Calculate v1 · v3. Are v1 and v2 linearly independent, orthogonal, both, or neither?
2. The goal of this problem is to find the eigenvalues and choose orthogonal eigenvectors for the following matrix:
(a) Find the eigenvalues of C. (There are two distinct eigenvalues; one negative and one positive. The positive e'genvaltie appears as a dou¬ble root of the characteristic equation.)
(b) Find an eigenvector v1 corresponding to the negative eigenvalue.
(c) Find an eigenvector v3 corresponding to the positive eigenvalue. It should be orthogonal to v1. Why?
(d) Find another cigenvector v3 corresponding to the positive eigenvalue. Choose it to be orthogonal to both v1 and v2.
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