Let A = (aij ) be the 23 × 23 real matrix defined by aij = 23 for all i, j. Let LA : R 23 → R 23 denote the linear operator defined by LA(x) = Ax. (a) Show that the vector v = (1, 1, . . . , 1) ∈ R 23...

Let A = (aij ) be the 23 × 23 real matrix defined by aij = 23 for all i, j.
Let LA : R 23 → R 23 denote the linear operator defined by LA(x) = Ax.
(a) Show that the vector v = (1, 1, . . . , 1) ∈ R
23 is an eigenvector of A.
(b) Show that A is diagonalizable, and describe a basis β such that [LA]β is diagonal