forms a subspace of all
What is the dimension of W? Find a basis for W.
To show that W, the set of all
forms asubspace of all
Now we know that M, the set of all
Let A, B in W with
and k be a scalar. Now,
Once again,
Therefore, W is a subspace of M. Now let x is a typical element of W, with
can be written as
where
Now for any linear combination
imply
Therefore,
hence dim
Find an explicit description of Nul A by listing vectors that span the null space.
Assume that A is row equivalent to B. Find bases for Nul A and Col A.
3.1 where 1 is repeating