A 2×2 matrix has eigenvalues 3 and -3. What are the trace and determinant?
Answer and explanation
Correct answer: B. trace 0, determinant -9
- Step 1: The trace equals the sum of the eigenvalues and the determinant equals their product. Step 2. Sum = 0, product = -9. Answer: trace 0, determinant -9. Why not the others: trace -9, determinant 0 is what you get if you swap the two quantities. trace 6, determinant -9 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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