Final answer:
The determinant of F and trace of G cannot be calculated without knowing the matrices. The inverse of F and eigenvalues of G require the matrices to be provided.
Step-by-step explanation:
a. Determinant of F:
To find the determinant of matrix F, you can use the formula ad - bc, where a, b, c, and d are the elements of the matrix.
In this case, the matrix F is not provided, so it is not possible to calculate the determinant.
b. Trace of G:
The trace of a matrix is the sum of its diagonal elements. Without knowing the matrix G, we cannot calculate its trace.
c. Inverse of F:
To find the inverse of a matrix, you need to apply the formula A^(-1) = (1/det(A)) * adj(A), where det(A) is the determinant of matrix A and adj(A) is the adjugate of matrix A. Without the matrix F, we cannot calculate its inverse.
d. Eigenvalues of G:
To calculate the eigenvalues of a matrix, you need to find the values of lambda for which the equation (G - lambdaI)x = 0 has non-trivial solutions, where G is the matrix, lambda is the eigenvalue, I is the identity matrix, and x is a non-zero vector. Without knowing the matrix G, we cannot calculate its eigenvalues.