2. True or false (circle one: T F a homogeneous VDE has a nondefective constant

Question

2. True or false (circle one: T F a homogeneous VDE has a nondefective constant coefficient matrix, the general solution does not require any generalized eigenvectors. rule explains how to develop trial solutions when using the method to solve nonhomogeneous differential b. The modification variation-of-parameters equations. TF c· The vector differential equation R'= As+ 6 is called homogeneous if b-6 . T F d. A polynomial differential operator satisfying P(D)F annihilate F(x). e. The general solution set. solution to a homogeneous VDE is also known as a fundamental T F f. Differentiation and integration of column n-vector functions are perfo componentwise T F Associated with a constant-coefficient nth-order linear differential equation is an nth-order polynomial equation known as the auxiliary equation. g. T F h. The general solution of a nonhomogeneous VDE consists of the general solution to the associated homogeneous VDE plus any particular solution to the nonhomogeneous equation. TF i. A matrix whose entries are functions of a single independent variable is known as a matrix function. TF

Explanation / Answer

(a) it is true , yes it is true when non-defective constant coefficient matrix , the generalized solution solution does not require any eigen-vectors.

(b) i don't know

(c) it is true , in non-homogenous case we require b so, it is true statement.

(d) it is true , also called annihilate F(x).

(e) it is false

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