Question

pls help, how to define trivial solution and nontrivial solution? in linear algebra..

Answer 1

trivial solution is when the solution vector is the zero vector as it satisfies every matrix equation

Answer 2

nontrivial is any non-zero solution

Answer 3

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

Answer 4

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

Answer 5

maybe if u showed me the system it wud be clearer

Answer 6

\[V1=(3,-1),V2(-2,2) its trivial solution..?\]

Answer 7

surely that is non-trivial? or do they mean the vectors which span the nullspace thus giving zero upon multiplication

Answer 8

that is the question..im using C1V1+C2V2=0 formula i get C1=0 and C2=0

Answer 9

c1=0 asnd c2 =0 is the trivial solution alright any non-zero values for the c's will be non-trivial

Answer 10

alright...thx u...:D

Answer 11

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