A 2×2 matrix has eigenvalues 4 and -4. What are the trace and determinant?
Answer and explanation
Correct answer: D. trace 0, determinant -16
- Step 1: The trace equals the sum of the eigenvalues and the determinant equals their product. Step 2. Sum = 0, product = -16. Answer: trace 0, determinant -16. Why not the others: trace -16, determinant 0 is what you get if you swap the two quantities. trace 8, determinant -16 is what you get if you subtract the eigenvalues. trace 0, determinant 0 is what you get if you use the sum twice.
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