1. Test the system below for controllability using three tests: (a) Find the controllability matrix P. Is rank (P)=n? =n) for (b) Find the matrix P₁ = [sI-A B]. This matrix contains s, not just numbers. Is rank ([SI-A B])= all s? If the system were discrete, would answer the change (i.e., would rank ([zI - A B]) change)? (c) Check if (i) the eigenvalues are distinct and (ii) B (or B if given system is already diagonalized) has no row that is all zeros. Recall that tests for cases with repeated eigenvalues exist but are not covered by this problem. -6 1 0 A-11 0 1,B=6 = [100], D = 0 -600 5 Recall PB AB A²B ... A"-B] (when B has more than one column each element will too.)