kaylarae1930
17.06.2020 •
Mathematics
Let f ( x ) = e x − cos x , f(x)=ex−cosx, g ( x ) = e x + cos x , g(x)=ex+cosx, and h ( x ) = cos x . h(x)=cosx. Are f ( x ) , f(x), g ( x ) , g(x), and h ( x ) h(x) linearly independent? If so, show it, if not, find a linear combination that works.
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Ответ:
No. f(x), g(x), & h(x) are linearly Dependent.
Step-by-step explanation:
f(x) = eˣ - cos(x) g(x) = eˣ + cos(x) h(x) = cos(x)
Create a 3 x 3 matrix where row 1 is x = 0, row 2 is x = π/2, row 3 = π
then find the determinant.
If det = 0 ⇒ dependent.
If det ≠ 0 ⇒ independent.
Since determinant = 0, they are linearly dependent.
There are an infinite number of possibilities to make them independent. Any change that makes the determinant ≠ 0
One example would be to make h(x) = sin(x)
Ответ:
1.) -2r - 7r = 9 -2r -7r = -9r r = -1
Step-by-step explanation: