Create matrices J2, J3, ..., J5 that are 2x2, 3x3, ..., 5x5,
with every entry being 1 in each matrix. For example
┌ ┐
J2 = │ 1 1 │ .
│ 1 1 │
└ ┘
Choose EIGENVALUES under MATRIX OPERATIONS in LINALG, then choose CHARACTERISTIC POLYNOMIAL and find the characteristic polynomial of each matrix. Use it to determine the eigenvalues.
Then, for each eigenvalue, use the procedure on p. 253 of the text to find a set of independent eigenvectors by choosing LINEAR EQUATIONS, then SOLVE. (You will first have to form the coefficient matrix, then augment it with a column of 0's.) Use your independent eigenvectors to form a matrix P as on p. 258 of the text (for J2 form P2, etc.).
Choose OTHER OPERATIONS, then SIMILARITY TRANSFORMATION, and obtain the similarity transform of J2 by P2, J3 by P3, etc.
Based on the information gathered make an educated guess about the nxn matrix Jn and its eigenvalues, etc.
