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Asked Nov 7, 2019
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Exercise 3.3.4. Verify that et and
1e2t are linearly independent. Hint: You must be a
et and
bit more tricky than in the previous exercise.
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Exercise 3.3.4. Verify that et and 1e2t are linearly independent. Hint: You must be a et and bit more tricky than in the previous exercise.

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Expert Answer

Step 1

First take the three vectors:

e'
e1
e'
0
1
y =e-1
-e'
1
1
ye- -e?
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e' e1 e' 0 1 y =e-1 -e' 1 1 ye- -e?

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Step 2

 

Find the wronskian of y1 , y2 and y3 ,

...
le
e'
e2
W(y y)= \ -e
-e2
0
e'
e2
=(-e +e")-e(e)+ e" (e" )
=-e" +e
=0
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le e' e2 W(y y)= \ -e -e2 0 e' e2 =(-e +e")-e(e)+ e" (e" ) =-e" +e =0

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