A 2×2 matrix has eigenvalues -1 and 5. What are the trace and determinant?
Answer and explanation
Correct answer: D. trace 4, determinant -5
- Step 1: The trace equals the sum of the eigenvalues and the determinant equals their product. Step 2. Sum = 4, product = -5. Answer: trace 4, determinant -5. Why not the others: trace -5, determinant 4 is what you get if you swap the two quantities. trace -6, determinant -5 is what you get if you subtract the eigenvalues. trace 4, determinant 4 is what you get if you use the sum twice.
Practise more Linear algebra, calculus and probability.
Free questions with an explanation for every one, and full timed GATE mock tests.
More Linear algebra, calculus and probability questions
- What is the rank of the matrix with rows (3, 6, 9); (6, 12, 18); (9, 18, 27)?
- If P(A and B) = 0.05 and P(B) = 0.5, what is P(A given B)?
- Find the divergence of F = (x², y², z²) at the point (1, 2, 2).
- The solution of dy/dx = −6y with y(0) = 6 is
- How many labelled spanning trees does the complete graph K7 have?
- How many functions are there from a set of 5 elements to a set of 6 elements?