Final answer:
To find the value of k for which the matrix A has one real eigenvalue of algebraic multiplicity 2, we need to find the eigenvalues and solve for k using the given equation.
Step-by-step explanation:
To find the value of k for which the matrix A = 6 ,k, 9, -9 has one real eigenvalue of algebraic multiplicity 2, we need to find the eigenvalues of the matrix.
The eigenvalues are the values of z that satisfy the equation: zî − ž (î − 2k) + 2 ( −îĵ + k ) = z î − žî + ž k − 2ĵ + k z.
By simplifying and comparing the coefficients of the variables, we can determine the value of k.