I have spent nearly the last hour trying to do this and im really stuck, the question is:

Determine the dimension of the subspace spanned by the set

{ [1,−1,0], [6,−2,3], [6,−1,4] }.

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- May 3rd 2008, 11:07 AMkbartlettDimension of the subspace?
I have spent nearly the last hour trying to do this and im really stuck, the question is:

Determine the dimension of the subspace spanned by the set

{ [1,−1,0], [6,−2,3], [6,−1,4] }. - May 3rd 2008, 11:21 AMflyingsquirrel
Hi

You should check the value of the determinant of the three vectors. Either it is 0 and at least one vector is a linear combination of the two others. In this case ,the dimension of the subspace may be 0, 1 or 2 but has it is neither 0 nor 1 (why ?) it'll necessarily be 2. Either the value is not 0 and the subspace has dimension 3.

$\displaystyle \left|\begin{array}{ccc}

1&6&6\\

-1&-2&-1\\

0&3&4

\end{array}\right|=\ldots$

Good Luck :D - May 4th 2008, 10:59 AMskamoni
The dimension of a basis for a subspace, is just the number of vectors contained in the basis, so in your case this would be 3.

- May 4th 2008, 11:14 AMIsomorphism
- May 4th 2008, 11:15 AMskamoni
Fair enough, row reduce it first then.

- May 6th 2008, 06:31 AMDr Zoidburg
It's cheating a little bit, but I've found this program extremely useful for these questions:

Linear Algebra Toolkit

It's an on-line Linear Algebra programme, one of which determines whether set of vectors S is linearly independent or linearly dependent.

For your problem it found that

...the set S = {**v**1,**v**2,**v**3} is**linearly independent**.

Consequently, the set**S forms a basis for span S**.

which should help you determine the dimension of the subspace