115年 - 115 國立嘉義大學_碩士班招生考試試題_電機工程學系：工程數學#143896

 (a) Is ODE F a Bernoulli ODE?

(b) Solve the ODE F

(a) Is ODE F a homogenous ODE?

(b) Solve the ODE F

三、Solve the following system of three equations in three variables by determining the inverse of the matrix of coefficients and then using matrix multiplication.

x₁+2x₂+3x₃=1

2x₁+5x₂+3x₃=3

x₁+8x₃=15

四、The set {(1, 2, 0, 3), (4, 0, 5, 8), (8, 1, 5, 6)} is linearly independent in R⁴. The vectors form a basis for a three-dimensional subspace V of R⁴. Construct an orthonormal basis for V.