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 matrixhas 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.