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Verify that ( \lambda_{i} ) is an eigenvalue of ( A ) and that ( mathbf{x}_{i} ) is a corresponding eigenvector. [ begin{array}{l} A=left[begin{array}{rrr} -2 & 2 & -3 2 & 1 & -6 -1 &

Answer 1

To verify that λi is an eigenvalue of A and xi is a corresponding eigenvector, we need to solve the equation (A - λiI)xi = 0, where I is the identity matrix.

Step-by-step explanation:

To verify that λi is an eigenvalue of A and that xi is a corresponding eigenvector, we need to solve the equation (A - λiI)xi = 0, where I is the identity matrix. Let's substitute the given values:

A - λiI = [-2-λi 2 -3 2 - λi 1 -6 -1 - λi]

Next, we can row-reduce the matrix to find its null space. If the null space contains non-zero vectors, then λi is an eigenvalue of A and xi is a corresponding eigenvector. If the null space only contains the zero vector, then λi is not an eigenvalue of A.