Thread: Subset and spanning

* Determine whether H, a subset of the vector space V, is a subspace of V:
a) V=M^n,n , H={A E M^n,n : det A does not =0}
b) V=P3, H={p E P3 : p(0)=0}


*If p1, p2,.....pm span Pn, write down a mathematical relationship between m and n.


Any help is greatly appreciated!!

Originally Posted by Jacko

* Determine whether H, a subset of the vector space V, is a subspace of V:
a) V=M^n,n , H={A E M^n,n : det A does not =0}

is the space of all matrices.

is the subset of of matrices with non-zero determinant.

To be a subspace must contain the zero matrix, but this has
zero determinant, so is not in so is not a subspace.

RonL

[quote=Jacko;68881b) V=P3, H={p E P3 : p(0)=0}
[/quote]

Please provide more explanation of you will leave us guessing at what your
notation means

RonL

Thanks for your help!
Sorry, the second part of the question is meant to read:
* Determine whether H, a subset of the vector space V, is a subspace of V:
V=P3 , H={p is an element of P3: p(0)=0}

I hope thats more clear

Originally Posted by Jacko

Thanks for your help!
Sorry, the second part of the question is meant to read:
* Determine whether H, a subset of the vector space V, is a subspace of V:
V=P3 , H={p is an element of P3: p(0)=0}

I hope thats more clear

If you said P3 is the space of polynomials of degree no grater than 3 that might help.

RonL

I have closed this thread as OP has double posted the second question in a new thread and already has responses there.

RonL