Answers to Quizlet 5.2

Question 1

Determine which of the following are true.

1. The determinant of a matrix A is the product of the diagonal entries. False. This is true for a triangular or diagonal matrix.
2. A row replacement on a matrix A does not change the eigenvalues. False. Since every square matrix can be reduced to an echelon matrix, which is a triangular matrix with 1s and 0s down the main diagonal (and thus has eigenvalues 0 and 1), this cannot be true.
3. Det(A^T) = -Det(A). False. Det(A^T) = +Det(A).

Question 2

Which of the following are eigenvalues of the matrix with rows, (6, -2, 0), (3, -2, 1), and (0, 4, 1)?

The choices were 5, 6, sqrt(6). The choices 5 and Sqrt(6) are eigenvalues. The number 6 is not an eigenvalue. The actual eigenvalues are 5, Sqrt(6), -Sqrt(6).

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