1. ## 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!!

2. 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}
$\displaystyle V$ is the space of all $\displaystyle n \times n$ matrices.

$\displaystyle H$ is the subset of $\displaystyle V$ of matrices with non-zero determinant.

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

RonL

3. [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

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

5. Originally Posted by Jacko
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

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

RonL