Consider the following functions. f,(x) = 0, 1,(x) = x, f,(x) = e* g(x) = c,f,(x) + czf2(x) + czf3(x) Solve for c,, C, and cz so that g(x) = 0 on the interval (-0, 0). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution (0, 0, 0}.) {C,, C2, C3} = Determine whether f,, f, fz are linearly independent on the interval (-, 0). O linearly dependent O linearly independent

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the following functions.
f,(x) = 0, f,(x) = x,
g(x) = c,f,(x) + c,f,(x) + czf;(x)
f3(x) = e*
Solve for c,, C,, and c, so that g(x) = 0 on the interval (-∞, ∞). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution {0, 0, 0}.)
{C,, C2, C3} = {
Determine whether f,, f,, fz are linearly independent on the interval (-0, o).
1'
linearly dependent
linearly independent
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Transcribed Image Text:Consider the following functions. f,(x) = 0, f,(x) = x, g(x) = c,f,(x) + c,f,(x) + czf;(x) f3(x) = e* Solve for c,, C,, and c, so that g(x) = 0 on the interval (-∞, ∞). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution {0, 0, 0}.) {C,, C2, C3} = { Determine whether f,, f,, fz are linearly independent on the interval (-0, o). 1' linearly dependent linearly independent Need Help? Read It
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