- #1

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I'm thinking it's Linear Dependent. Since it says that any linear combination must be 0.

a*x + b*y = 0, a = b = 0.

So for any integer x, the value is 0. So [-1, 1] works.

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- Thread starter AngeloG
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- #1

- 104

- 0

I'm thinking it's Linear Dependent. Since it says that any linear combination must be 0.

a*x + b*y = 0, a = b = 0.

So for any integer x, the value is 0. So [-1, 1] works.

- #2

HallsofIvy

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Also Linear Depence of a set of vectors does NOT mean "any linear combination must be 0". Only that there exist at least one more linear combination other than the one where all coefficients are 0. In order that two functions, f and g, be dependent, there must be a and b,

But still, what

- #3

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The question is:

Check the linear dependency of the functions sin(pi x).

Check the linear dependency of the functions sin(pi x).

- #4

Defennder

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You said "functions" but there's only one non-zero function. What kind of values can x take?

- #5

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1, cos(pi x), sin(pi x).

Those are the functions. 1 is linear independent, cos(pi x) and sin(pi x) I'm not sure about.

- #6

HallsofIvy

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If you don't even know enough to quote the problem correctly, then I strongly recommend you review what "dependent" and "independent" mean! Once again, a **single** function (vector) is **always** "independent"! It makes no sense at all to say "1 is linearly independent" and, again, the problem is NOT asking about the "dependence" or "independence" of the **each** of those three functions. It is asking, as I suggested before, about the dependence or independence of the **set** of those three functions.

Now, how does your text book**define** "dependent functions" or "dependent vectors"?

Now, how does your text book

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