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Which of the following is/are the eigenvector(s) for the matrix given below? [-9, -6, -2, -4; -8, -6, -3, -1; 20, 15, 8, 5; 32, 21, 7, 12]

1. [-1; 1; 0; 1]
2. [1; 0; -1; 0]
3. [-1; 0; 2; 2]
4. [0; 1; -3; 0]

Correct answer: [-1; 1; 0; 1]

Solution

The vector (-1, 1, 0, 1) satisfies the eigenvalue equation for the given matrix, indicating that it is a valid eigenvector. This means that when the matrix is multiplied by this vector, the result is a scalar multiple of the vector itself, confirming its eigenvector status.

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