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notka56 [123]
2 years ago
15

Determine whether the given set of functions is linearly independent on the interval (−[infinity], [infinity]). f1(x) = x, f2(x)

= x2, f3(x) = 6x − 2x2 linearly dependent linearly independent
Mathematics
1 answer:
ziro4ka [17]2 years ago
3 0

The given set of functions are not linearly independent.

Given,

f_{1} (x) = x\\f_{2} (x) = x^{2} \\f_{3} (x) = 6x-2x^{2}

We need,

c_{1} f_{1} (x)+c_{2} f_{2} (x)+c_{3} f_{3}(x)=0

Substituting the values in equation we get,

c_{1} x+c_{2} x^{2} +c_{3} (6x-2x^{2} )=0\\

Computing the equation we get,

c_{1} x+c_{2} x^{2} +c_{3} 6x-c_{3} 2x^{2}=0

(c_{1} +6c_{3} )x+(c_{2} -2c_{3} x^{2} =0

This resolves to two equations

(c_{1} +6c_{3})x =0\\(c_{2} -2c_{3} )x^{2} =0

These will have an infinite set of solutions:

c_{1} =-6c_{3} \\c_{2} =2c_{3}

Two functions are said to be linearly independent if neither function is a constant multiple of the other.

Here, it is clear that the given functions are not linearly independent.

Learn more about linearly dependent or independent functions here:brainly.com/question/18331568

#SPJ4

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Greetings,

<em>I hope you and your family are staying safe and healthy! </em>

Answer: x = -1 and y = 3

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