Question

The determinant of a 2x2 matrix is 50. If one eigenvalue of the matrix is 10, the other eigen value is

(A) 5 (B) 10 (C) 50 (D) none​

Answer 1

Answer:

Determinant of matrix =product of eigen values

50= 10 x value

Value =50/10

Value =5

Answer 2

Given:

Determinant of the matrix=50

One eigenvalue of the matrix=10

To Find:

The other eigenvalue

Solution:

The determinant of a 2×2 matrix is equal to the product of its eigenvalues.

Let the other eigenvalue be b

⇒10×b=50

⇒b=5

Hence, the other eigenvalue is 5. (Option a)