For a $3 \times 3$ matrix $A$ with eigenvalues $\lambda_1 = 1$, $\lambda_2 = 2$, $\lambda_3 = -1$, the coefficients of the characteristic polynomial $\chi(\lambda) = -\lambda^3 + c_2\lambda^2 + c_1\lambda + c_0$ are determined by elementary symmetric polynomials in the eigenvalues. Which is true?