Re: Mathematical fact about determinants (Shri)

[James Crook]

Shri,

Thanks.  What about a non-invertible matrix?  Is the fact still true?  Also please describe what 'elementary row operations' are OK - what operations are allowed and what aren't?  I'm worried that one of the operations you might have in mind does not preserve determinants.  If you use it without realizing that, you could get into trouble in a proof about determinants.

And thanks for being patient with me about me thinking you were starting out on task 2.  I really should have realized :)  .

--James.

On 15 June 2011 07:19, Shri R Ganeshram <sh...@mit.edu> wrote:

James,
My message was the mathematical fact. :) I think the inverse matrix talk inspired that ("primed me").
It was not the solution to the second part.
"The determinant of an invertible matrix is the same as the determinant of that matrix after undergoing elementary row operations. Aka, given matrix A, invertible, and a set of row operations R, and that B is R(A), det A= det B.

I'm not sure how well I phrased that, but I think the point of the exercise was to draw from knowledge and not from an outside source. :)

-Shri"
-Shri

[James Crook]

Shri,

Thanks for the update.

So "Multiplying one row by a constant c and adding it to another row"
preserves the determinant.
Multiplying one row by a constant, multiplies the determinant by that
constant.
Swapping two rows multiplies the determinant by -1.

This is all true for invertible matrices.
What about non invertible matrices? What happens then?

--James.

[shr...@gmail.com]

This would hold true for noninvertible matrices as well, implying that elementary row operations would continuously yield a determinant of zero.