Could use matlab if need it.

The characteristic polynomial of the A matrix for an LTI dynamic system can be written as r(1) = (12+21+10)(1+3)3. You also know that the rank of (A+31) is 4. = Let P be the matrix which will transform A to an appropriate real block modal form. Assume the P matrix is such that the components of the model form arising from the complex eigenvalues will be located in the upper left corner. a.) Compute the matrix P-1,At P. b.) Suppose that we identify the outputs of this system to be y(t) = P-'x(t). If the initial condition is xo = P4 where P4 is the fourth column of the P matrix, find y(t) explicitly as a function of time. e 1 = c.) Suppose in b) that the initial condition is instead Xo = P2. Find y(t). The characteristic polynomial of the A matrix for an LTI dynamic system can be written as r(1) = (12+21+10)(1+3)3. You also know that the rank of (A+31) is 4. = Let P be the matrix which will transform A to an appropriate real block modal form. Assume the P matrix is such that the components of the model form arising from the complex eigenvalues will be located in the upper left corner. a.) Compute the matrix P-1,At P. b.) Suppose that we identify the outputs of this system to be y(t) = P-'x(t). If the initial condition is xo = P4 where P4 is the fourth column of the P matrix, find y(t) explicitly as a function of time. e 1 = c.) Suppose in b) that the initial condition is instead Xo = P2. Find y(t)