1. The problem asks whether some equations cannot be solved by the conjugate gradient method. 2. The conjugate gradient method is an iterative algorithm used to solve systems of linear equations of the form $$Ax = b$$ where: - $$A$$ is a symmetric positive-definite matrix. - $$x$$ is the vector of unknowns. - $$b$$ is the known vector. 3. Important rule: The conjugate gradient method requires $$A$$ to be symmetric and positive-definite. If $$A$$ is not symmetric or not positive-definite, the method may fail or not converge. 4. Therefore, equations with matrices that are: - Non-symmetric, - Indefinite (not positive-definite), or - Singular (not invertible) cannot be reliably solved by the conjugate gradient method. 5. In summary, the conjugate gradient method is limited to solving linear systems with symmetric positive-definite matrices. Other types of systems require different methods.