Question

hey guys,
can someone explain me what he does when he says "Now we need to set the coefficients equal. Doing this gives". it's pretty obvious that you would get (Ab-a=0) by using t=0
but what is he using at the other part?..im confused
Here's the link: http://tutorial.math.lamar.edu/Classes/DE/NonhomogeneousSystems.aspx

Answer 1

KingGeorge please can you help me with my calculuc problem

Answer 2

Looking at that link, he has an equation where \[\vec{0}=t(A\vec{a}+\vec{g})+(A\vec{b}-\vec{a})\]He then sets the coefficients of \(t\) and \(t^0\) equal to each other on both sides of the equation. The LHS obviously has the coefficients as 0 since you have the zero vector. So \[A\vec{a}+\vec{g}=0\]and\[A\vec{b}-\vec{a}=0\]

Answer 3

For example, if \(A\vec{a}+\vec{g}\neq0\), then the LHS, instead of being 0, would have to have a nonzero coefficient for the \(t\) term.

Answer 4

thx a lot george!!!!

Answer 5

You're welcome.