Given a 3×3 symmetric real matrix A, we define f(A) as a 3×3 matrix with the same eigenvectors of A such that if A has eigenvalues a, b, c, then f(A) has eigenvalues b+c, c+a, a+b (in that order). We define a sequence of symmetric real 3×3 matrices A0,A1,A2,… such that An+1=f(An) for n≥0. If the matrix A0 has no zero entries, determine the maximum number of indices j≥0 for which the matrix Aj has any null entries. linear algebramatrixSequencessymmetric matrixeigenvalue and eigenvector