For matrix A below, make a change of variables that decouples the equation x' = Ax. Write the equation x(t) = Py(t) that leads to the uncoupled system y' = Dy, specifying P and D.
A = [[10, -3], [5, 2]]
Choose the correct values of P and D below that result in the decoupled system y' = Dy when x(t) = Py(t).
A. P = [[-5, 1], [-3, 1]], D = [[7, 0], [0, 5]]
B. P = [[3, 1], [5, 1]], D = [[7, 0], [0, 5]]
C. P = [[3, 1], [5, 1]], D = [[5, 0], [0, 7]]
D. P = [[1, -3], [1, 5]], D = [[5, 0], [0, 7]]
Write the equation x(t) = Py(t) using the matrix P found above.
x(t) = []y(t)