For matrix B = [[9, -2], [-2, 6]], one of the eigenvalues is 5. Then, the other eigenvalue is
A. 2
B. 10
C. 8
D. 6

Question

Accepted Answer

Second eigenvalue = 10. Answer: B. For any square matrix, the sum of all eigenvalues equals the trace (sum of diagonal elements). If one eigenvalue is known, the other can be found by subtracting from the trace. Here trace(B) = 9 + 6 = 15, so if one eigenvalue is 5, the other is 15 - 5 = 10.

For matrix B = [[9, -2], [-2, 6]], one of the eigenvalues is 5. Then, the other eigenvalue is A. 2 B. 10 C. 8 D. 6