True-False Review For Questions (a)-(j), 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 in fact from the text. If false, provide an example, illustration, or brief explanation of why the statement is false. If y 1 , y 2 , ⋯ , y n are solutions to a regular n th -order linear homogenous differential equation such that W [ y 1 , y 2 , ⋯ , y n ] ( x ) is zero at some points of I and nonzero at other points of I , then { y 1 , y 2 , ⋯ , y n } is a linearly independent set of functions.
True-False Review For Questions (a)-(j), 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 in fact from the text. If false, provide an example, illustration, or brief explanation of why the statement is false. If y 1 , y 2 , ⋯ , y n are solutions to a regular n th -order linear homogenous differential equation such that W [ y 1 , y 2 , ⋯ , y n ] ( x ) is zero at some points of I and nonzero at other points of I , then { y 1 , y 2 , ⋯ , y n } is a linearly independent set of functions.
Solution Summary: The author explains that if the statement "if y_1,.., is a linearly independent set of function" is true or false.
For Questions (a)-(j), 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 in fact from the text. If false, provide an example, illustration, or brief explanation of why the statement is false.
If
y
1
,
y
2
,
⋯
,
y
n
are solutions to a regular
n
th
-order linear homogenous differential equation such that
W
[
y
1
,
y
2
,
⋯
,
y
n
]
(
x
)
is zero at some points of
I
and nonzero at other points of
I
, then
{
y
1
,
y
2
,
⋯
,
y
n
}
is a linearly independent set of functions.
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