Find the recurrence relation and use it to generate the first five terms of the series of
the general solution for y′′− xy′+ y = 3 .
Solve the initial value problem
Find the general solution of the equation
xy′+ (x − 2) y = 3x3e−x
Determine the relation between the nonzero constant parameters a and b such that
(1) a straight line.
(2) a circle.
Suppose that matrix A∈ Rn×n is nonsingular and λ∈C is an eigenvalue of A .
Prove that 1/λ is an eigenvalue of A−1 .
Let λ1 and λ2 be distinct real eigenvalues of matrix A∈Rn×n . Suppose that
Av1 = λ1v1 and Av2 = λ2v2 for some nonzero vectors v1,v2 ∈ Rn . Please show that
v1 and v2 are linearly independent. (Note that λ1 ≠ λ2)
Suppose that A∈Cn×n is a unitary matrix. Prove that | det(A−1) |= 1.
可觀看題目詳解,並提供模擬測驗!(免費會員無法觀看研究所試題解答)