110年 - 110 國立臺灣大學_碩士班招生考試_ 工程科學及海洋工程學研究所丙組:工程數學(L)#100704

1. (25%) Show that the equation is exact, and obtain its general solution. Also, find the particular solution corresponding to the given initial condition as well.
  

4. (20%) It is known that the nxn tridiagonal matrix

has eigenvalues
for j=1,2,... ..,n. (A is called tridiagonal because all elements are zero except for those on the main diagonal and the two adjacent diagonals.)
Verify Bquation (1) by calculating the eigenvalues for n = 1 and n = 2.