Let
A=[113151311]A = \begin{bmatrix} 1 & 1 & 3 \\ 1 & 5 & 1 \\ 3 & 1 & 1 \end{bmatrix}A=113151311
All three eigenvalues of AAA are integers.
Compute det(A+3I)\det(A + 3I)det(A+3I) and tr(A3)\operatorname{tr}(A^3)tr(A3).
Select all that apply.
det(A+3I)=54\det(A+3I) = 54det(A+3I)=54 and tr(A3)=235\operatorname{tr}(A^3) = 235tr(A3)=235
det(A+3I)=54\det(A+3I) = 54det(A+3I)=54 and tr(A3)=343\operatorname{tr}(A^3) = 343tr(A3)=343
det(A+3I)=0\det(A+3I) = 0det(A+3I)=0 and tr(A3)=235\operatorname{tr}(A^3) = 235tr(A3)=235
det(A+3I)=−9\det(A+3I) = -9det(A+3I)=−9 and tr(A3)=235\operatorname{tr}(A^3) = 235tr(A3)=235