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DochEvi [55]
2 years ago
10

Find the wronskian of the set {1 - x, 1 + x, 1 - 3x}.​

Mathematics
2 answers:
bija089 [108]2 years ago
8 0

Answer:

Correct option is

A

−415

1(x+1x−1)=3x

⇒x+1x−1=3⇒x+1x−1=9

x−1=9x+9

−8x=10⇒x=4−5

f(3)=3(4−5)=4−15

Levart [38]2 years ago
3 0

Step-by-step explanation:

\red{\large\underline{\sf{Solution-}}}

We know that,

\rm :\longmapsto\:Wronkian \: of \: the \: set \: {\left \{f_{1}(x),f_{2}(x),f_{3}(x) \right \}} \: is \:

W{\left(f_{1},f_{2},f_{3} \right)}\left(x\right) = \left|\begin{array}{ccc}f_{1}\left(x\right) & f_{2}\left(x\right) & f_{3}\left(x\right)\\f_{1}^{\prime}\left(x\right) & f_{2}^{\prime}\left(x\right) & f_{3}^{\prime}\left(x\right)\\f_{1}^{\prime\prime}\left(x\right) & f_{2}^{\prime\prime}\left(x\right) & f_{3}^{\prime\prime}\left(x\right)\end{array}\right|

Here,

\rm :\longmapsto\:f_1(x) = 1 - x

\rm :\longmapsto\:f_2(x) = 1  +  x

\rm :\longmapsto\:f_3(x) = 1 - 3x

So, there respective differential coefficients are as follow

\rm :\longmapsto\:f_1'(x) = 0 - 1 =  - 1

\rm :\longmapsto\:f_2'(x) = 0  +  1 =   1

\rm :\longmapsto\:f_3'(x) = 0 - 3 =    - 3

Also,

\rm :\longmapsto\:f_1''(x) = 0

\rm :\longmapsto\:f_2''(x) = 0

\rm :\longmapsto\:f_3''(x) = 0

So, on substituting the values in

W{\left(f_{1},f_{2},f_{3} \right)}\left(x\right) = \left|\begin{array}{ccc}f_{1}\left(x\right) & f_{2}\left(x\right) & f_{3}\left(x\right)\\f_{1}^{\prime}\left(x\right) & f_{2}^{\prime}\left(x\right) & f_{3}^{\prime}\left(x\right)\\f_{1}^{\prime\prime}\left(x\right) & f_{2}^{\prime\prime}\left(x\right) & f_{3}^{\prime\prime}\left(x\right)\end{array}\right|.

We get

\rm :\longmapsto\:W=  \:  \ \: \begin{gathered}\sf \left | \begin{array}{ccc}1 - x&1 + x&1 - 3x\\ - 1&1& - 3\\0&0&0\end{array}\right | \end{gathered} \\

\rm \:  =  \: 0

[ If elements of any row all are 0, its determinant value is zero]

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Note: The formula for the place to find the median is "([the number of data points] + 1) ÷ 2", but you don't have to use this formula. You can just count in from both ends of the list until you meet in the middle, if you prefer, especially if your list is short. Either way will work.

Step-by-step explanation:

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