Week 9: Part 1: Show that there is no relationship between any kind of row operation and the eigenvalues of the matrices involved as follows. For each of the three types of row operation cR; + R; → R;, cR; → Rj, and R; + R; which are adding two rows, multiplying a row by a scalar, and switching two rows: Find four matrices (for a total of 12 matrices) A, B, C, D such that A B and C # D and also A ~ B and C ~ D, the matrix A is row equivalent to B via exactly one row operation of the appropriate type, and also C is row equivalent to D via exactly one row operation of the appropriate type, and such that A and B have the exact same eigenvalues but C and D have different eigenvalues, and be sure to state all eigenvalues. Conclude that there is no relationship whatsoever between two matrices "being row equivalent" and "have the same eigenvalues".