Finding Determinant

Algebra Level 3

If $A$ is a $5\times 5$ real matrix with trace 15 and if 2 and 3 are eigenvalues of $A$ , each with algebraic multiplicity 2, then the determinant of $A$ is equal to $\text{\_\_\_\_\_\_\_\_\_\_}$ .

120 24 180 0

1 solution

Otto Bretscher
Feb 14, 2016

Since the trace is the sum of the eigenvalues, the "missing" eigenvalue is $15-2*2-2*3=5$ . Now the determinant is the product of the eigenvalues, $\det(A)= 2^2*3^2*5=\boxed{180}$

Finding Determinant

1 solution

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