(10 points) 8. True or false (circle one Annihilators are used in conjunction wi
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Question
(10 points) 8. True or false (circle one Annihilators are used in conjunction with the method of undetermined coefficients to solve certain nonhomogeneous linear differential equations a. T F b. The transition matrix for a VDE is the fundamental matrix which equals the identity matrix when the independent variable is zero. TF The general solution of a nonhomogeneous differential equation of order n consists of the general solution to the associated homogeneous equation plus c. ion to the nonhomogeneous equation. Linear dependence of n column n-vector functions may be determined by computing the Wronskian of those functions. d· T F Another name for a linear differential operator is a polynomial differential operator e. Given a nonhomogeneous differential equation, the solution to the associated he t. function. An nh order linear differential equation is equivalent to a firnst-order linear system of differential equations & T F h. The general solution to a first-order linear system in n unknown functions is a vector space of dimension n A first-order linear system of differential equations together with conditions of the form x"(.) = , for each function x, (r) is known as an initial-value problem. i. j. A square matrix whose columns are linearly independent solutions to a given homogeneous vector differential equation is known as a fundamental matrix T FExplanation / Answer
1.Annihilators are used in conjunction with the method of undetermined to solve certain nonhomogeneous linear differential equation- true
2.The transition matrix for VDE is the fundamental matrix which equals the identity matrix when independent variable is zero.-False
3.The general solution of a non homogeneous differential equation of order n consists of the general solution to the associated homogeneous equation plus any particular solution to the non-homogeneous solution.-True
4.The linear dependence of n column n vector function may be determined by computing the wronskian of those functions.-True
5.Another name for linear differential operator is a polynomial differential operator.-True
6.Given a non-homogeneous differential equation, the solution to a associated homogeneous equation is known as a supplementary function.-False
7.An nth order linear differential equation is equal to the first order of linear system of differential equation.-True
8.The general solution to a first order linear system in n unknown functions is a vector space of diamention n.-True
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