anonymous
  • anonymous
pls help, how to define trivial solution and nontrivial solution? in linear algebra..
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
trivial solution is when the solution vector is the zero vector as it satisfies every matrix equation
anonymous
  • anonymous
nontrivial is any non-zero solution
anonymous
  • anonymous
for example of u are finding the nullspace of a matrix the zero vector is in the nullspace of every matrix so it is a trivial solution

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anonymous
  • anonymous
for an exmple i got 2 solution a=0, b=0 that means its trivial..? how about matrix independent and matrix dependent...? thx for helping
anonymous
  • anonymous
maybe if u showed me the system it wud be clearer
anonymous
  • anonymous
\[V1=(3,-1),V2(-2,2) its trivial solution..?\]
anonymous
  • anonymous
surely that is non-trivial? or do they mean the vectors which span the nullspace thus giving zero upon multiplication
anonymous
  • anonymous
that is the question..im using C1V1+C2V2=0 formula i get C1=0 and C2=0
anonymous
  • anonymous
c1=0 asnd c2 =0 is the trivial solution alright any non-zero values for the c's will be non-trivial
anonymous
  • anonymous
alright...thx u...:D
anonymous
  • anonymous
if the 2 vectors are linearly independent there will only be the trivial solution and they are as the matrix they form is row equivalent to the identity matrix

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