Applications of Diagonalization of Matrices

page-1

page-2

Order of Solving

1. First, we take Final and Initial Condition Matrices, assign them names t and s.
2. Then we make another matrix t-s.
3. Now, we make an augmented matrix of every switch possibility with matrix t-s as columns.
4. Calculate Row Echelon Form(REF) of the augmented matrix using internet matrix solver.
5. Solve the REF to obtain values for x1, x2, …, x10.
6. If x1, x2, …, x10 have even value, this means the switch is not to be pressed, otherwise switch is to be
   pressed. Thus -1 and 1 means that the switch needs to be pressed, and 0 means the switch does not need to be
   pressed.
   Note: The order of switches does not matter as we concluded above.

page-3

page-4

page-5

page-6