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Topic: Failing Linear Algebra:
Replies: 54   Last Post: Jan 10, 2007 12:47 PM

 Messages: [ Previous | Next ]
 Russell Blackadar Posts: 586 Registered: 12/12/04
Re: Failing Linear Algebra:
Posted: Apr 30, 2004 10:42 AM

I see that I forgot to address one point in my earlier reply.

On 29 Apr 2004 20:35:59 GMT, Anonymous wrote:

[snip]

>Yes. We call all of the variables that appear first in any of the equations,
>when the system is in echelon form, "basic variables". The other ones are
>called "free variables". So, in any system in echelon form, the number of
>basic variables equals the number of equations. Is that what you mean by
>"n-r", where r is the number of free variables (dimension of the kernel)?

Yes, you understood me correctly here, but as I said in a followup, it
would have been less confusing if I had chosen a different letter than
r since my notational choice is probably opposite to what you will
find in books. So, let's use k instead. With that change, k is the
number of free variables (dimension of the kernel) and n-k is the
number of basic variables.

Or,
>is your "r" actually the basic variables and "n-r" the frees?

The rank of the matrix (frequently denoted r, though not in my
previous posting) is the number of independent equations in the
system, same as the number of basic variables, and same as the
dimension of the image.

I hope you don't come away from this with the vague feeling that this
is all very confusing. It's really as simple as can be. I apologize
for my notational blunder; pretend that I wrote "k" in my earlier post
and you shouldn't get confused.

Date Subject Author
4/22/04 Guest
4/22/04 Michael N. Christoff
1/10/07 Gerry Myerson
1/10/07 Jonathan Miller
1/10/07 Guest
1/10/07 David C. Ullrich
1/10/07 Acid Pooh
1/10/07 Guest
4/23/04 Brian Borchers
4/27/04 Guest
1/10/07 maky m.
4/26/04 David Ames
1/10/07 Guest
1/10/07 Michael Stemper
1/10/07 maky m.
4/23/04 Porker899
4/27/04 Guest
1/10/07 Abraham Buckingham
1/10/07 Mitch Harris
1/10/07 Guest
1/10/07 Grey Knight
1/10/07 Guest
1/10/07 Toni Lassila
1/10/07 Thomas Nordhaus
1/10/07 George Cox
4/28/04 Dave Rusin
4/28/04 George Cox
4/28/04 George Cox
4/29/04 Marc Olschok
4/29/04 Mitch Harris
4/29/04 Robert Israel
4/28/04 Guest
4/29/04 Guest
1/10/07 Dave Rusin