Consider the following matrix:

A = [[2, 3],[x, y]]

If the eigenvalues of A are 4 and 8, then:

A. x = 4, y = 10
B. x =...

Question

Consider the following matrix:

A = [[2, 3],[x, y]]

If the eigenvalues of A are 4 and 8, then:

A. x = 4, y = 10
B. x = 5, y = 8
C. x = -3, y = 9
D. x = -4, y = 10

Accepted Answer

D. x = -4, y = 10 For a 2x2 matrix, the sum of eigenvalues equals the trace (sum of diagonal elements) and the product of eigenvalues equals the determinant. Using these two relationships with the known eigenvalues 4 and 8, we can set up two equations to solve for x and y.

Consider the following matrix: A = [[2, 3],[x, y]] If the eigenvalues of A are 4 and 8, then: A. x = 4, y = 10 B. x = 5, y = 8 C. x = -3, y = 9 D. x = -4, y = 10