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**1. The problem statement, all variables and given/known data**

Find the eigenvalues of B = [5 2 0 2], [3 2 1 0], [3 1 -2 4], [2 4 -1 2]. Compute the sum and product of eigenvalues and compare it with the trace and determinant of the matrix.

**2. Relevant equations**

**3. The attempt at a solution**

I get the characteristic polynomial x^4 -7x^3 - x^2 - 33x + 8. I used a computer program to solve it for 0 and got eigenvalues L1= 0.238 and L2= 7.673 roughly. Their sum is 7.911. Their product is 1.826. The trace of the matrix is 7. The determinant of the matrix is 8. The trace and the sum of the eigenvalues match up, approximately. The determinant and the product of the eigenvalues, however, don't. What am I doing wrong?