- #1
nhrock3
- 415
- 0
this is a two part question:
v1..vn is a basis
of R^n
and there is a vector b which belongs to R^n and b differs the sero vector
A.
proof that {v1-vn,v2-vn,...,vn-1 - vn}
by definition
in order to prove that a group is independant
we need to show the the only way for
a1(v1-vn)+a2(v2-vn) ..+an(vn-1 -vn)=0
is a1=..=an=0 all the coefficient hs to be zero
so it rang a bell "i need to get a trivial solution "
but trivilal solution is in Ax=0 system could be should if |A| differs zero.
but A is a square matrices by difinition.
how to construct from this single equation a square matrices?
??
the second question:
if v1..vn are solutions to Ax=b system then
rho(A)=1
??
rho(A) is the dimention of row or column space
if v1..vn are solving this system
then the dimention of the solution space is n dim(P(A))=n
and from the formula where n=dim(P(A))+rho(A) we get n=n+rho(A)
so i got
rho(A)=0
but i am asked to prove that rho(A)=1
where is my mistake
v1..vn is a basis
of R^n
and there is a vector b which belongs to R^n and b differs the sero vector
A.
proof that {v1-vn,v2-vn,...,vn-1 - vn}
by definition
in order to prove that a group is independant
we need to show the the only way for
a1(v1-vn)+a2(v2-vn) ..+an(vn-1 -vn)=0
is a1=..=an=0 all the coefficient hs to be zero
so it rang a bell "i need to get a trivial solution "
but trivilal solution is in Ax=0 system could be should if |A| differs zero.
but A is a square matrices by difinition.
how to construct from this single equation a square matrices?
??
the second question:
if v1..vn are solutions to Ax=b system then
rho(A)=1
??
rho(A) is the dimention of row or column space
if v1..vn are solving this system
then the dimention of the solution space is n dim(P(A))=n
and from the formula where n=dim(P(A))+rho(A) we get n=n+rho(A)
so i got
rho(A)=0
but i am asked to prove that rho(A)=1
where is my mistake