1) Let V be a vector space and
. Show that the following vectors are linearly dependent.
So is it...
[ 1 1 0 9 0 ][a] = [0]
[ 1 -3 1 0 23][b] = [0]
[ 1 6 0 7 -1][c] = [0]
[-44 0 1 5 -1][d] = [0]
?
Will that not give a=b=c=d=0,
Mr F says: Yes. Therefore the set is dependent.
which is not really a lot of use
Mr F says: yes it is.
because could that not just be applied to any combination of vectors?
Mr F says: Of these vectors, yes. Is it really that surprising that in a vector space V of dimension four, five vectors from V will always be linearly dependent?
I thought about using Gaussian elimination but again thats not gonna work and i dont know how to use it on an m x n (m not equal to n{whats the latex for this?}) matrix. So how do you do it?
2) Write w as the linear combination of the vectors
Now i can see almost straight away that
but im not sure if the correct method to actually solve these. Is there one? Guassian Elimination?