109年 - 109國立成功大學_碩士班招生_電機資訊學院：工程數學#103801

4. (10%) Find the Laplace transform of y(t).
  

5. (10%) Find the inverse Laplace transform of F(s)
  

6. (10%) Solve the following coupled differential equation.
 x+(a+By-aBx=0
y"-(a+8)x'-aBy=0,a＞0.8＞0,a≠β
x(0)=0,x'(0)=1
 y(0)=0,y'(0)=0. 

7. (20%) Assume we have collected the data from four types of sensors four times from two experiments. Put these data in the form of matrix A and B.
   
Check if matrix A and matrix B are diagonalizable. If it is diagonalizable, compute a matrix P such that

BP is a diagonal matrix and compute the determinant of A⁴-5A²+2I or B⁴-5B²+2I. I is an

identity matrix.

(a) What is the coordinate vector of with respect to A?