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anonymous
 5 years ago
Partial Differential Equation, first two.
anonymous
 5 years ago
Partial Differential Equation, first two.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Question 2 is fairly straight forward. Assuming, of course, that all the vectors \[Y_{1}, Y _{2}, Y _{3}\] are nonzero, let's see what happens if \[k _{3}\]is nonzero. We can rearrange the equation \[k _{1}Y _{1}+k _{2}Y _{2}+k _{3}Y _{3} = 0\] into \[Y _{3} =1/k _{3}(k _{1}Y _{1}k _{2}Y _{2})\] so that the right side is nonzero because the left is nonzero, and it is defined because \[k _{3}\neq0.\] Note that \[Y _{3}\] is now a linear combination of the other two vectors, or is in \[Span \left\{ Y _{1} ,Y _{2}\right\}\] if you prefer. Now do the same for the other two vectors.
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