CHAPTER 2 MATRICES Eigenvalues and Eigenvectors nhaaimksem 120162017eqt
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CHAPTER 2: MATRICES Eigenvalues and Eigenvectors nhaa/imk/sem 120162017/eqt 101/rk 12/32
EIGENVALUES & EIGENVECTORS Definition 2. 26 Consider the matrix A (Square Matrix). The eigenvalue, and the eigenvector X are defined by the equation: (1) Such that X is said to be an eigenvector and it must be a nonzero solution which correspond to the eigenvalue, nhaa/imk/sem 120162017/eqt 101/rk 12/32
EIGENVALUES & EIGENVECTORS To find the eigenvalues of matrix A, from (1) Since the eigenvectors, X is a nonzero solution, therefore the determinant of must be zero. The scalar, that satisfy eigenvalue of A. is called the nhaa/imk/sem 120162017/eqt 101/rk 12/32
EIGENVALUES & EIGENVECTORS Steps of Solutions (i) Compute (ii) For each eigenvalue, solving and get the eigenvalues : Find the eigenvectors by nhaa/imk/sem 120162017/eqt 101/rk 12/32
EIGENVALUES & EIGENVECTORS Example Consider matrix Find the eigenvalues and eigenvectors using Gaussian elimination method. nhaa/imk/sem 120162017/eqt 101/rk 12/32
EIGENVALUES & EIGENVECTORS Solution Step 1: Find eigenvalue by computing Step 2: Find eigenvectors corresponding to each eigenvalue. Apply Gauss elimination on nhaa/imk/sem 120162017/eqt 101/rk 12/32
EIGENVALUES & EIGENVECTORS Example Consider matrix Find the eigenvalues and eigenvectors using Gaussian elimination method. nhaa/imk/sem 120162017/eqt 101/rk 12/32
