decide if the given statement is true or false,and give a brief justification for your answer.If true, you can quote a relevant definition or theorem . If false,provide an example,illustration,or brief explanation of why the statement is false. (a) If X(t) is a fundamental matrix for x′ = Ax, then a particular solution to the nonhomogeneous vector differential equation x′ = Ax+b is xp(t) = X(t)u(t), where u(t) is any arbitrary vector function.
Vector Arithmetic
Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.
Vector Calculus
Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.
decide if the given statement is true or false,and give a brief justification for your answer.If true, you can quote a relevant definition or theorem . If false,provide an example,illustration,or brief explanation of why the statement is false.
(a) If X(t) is a fundamental matrix for x′ = Ax, then a particular solution to the nonhomogeneous vector differential equation x′ = Ax+b is xp(t) = X(t)u(t), where u(t) is any arbitrary vector function.
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