Algebra ?

[1123581321]

I was wondering what exactly 'standard form' is/means in the area of linear equations

[ajb]

[math]Ax + By = C[/math],

 

with A and B both nonzero, A, B, and C are integers whose greatest common factor is 1, and A is nonnegative.

[1123581321]

So standard form is simply the expression in its most basic form...

[khaled]

in Linear Algebra, a Linear Equation is an equation that geometrically forms a line,

 

1D: [latex]ax = c \rightarrow ax + 0y + 0z = c[/latex]

 

2D: [latex]ax + by = c \rightarrow ax + by + 0z = c[/latex]

 

3D: [latex]ax + by + dz = c[/latex]

 

Linear Equations can solved easily, Systems of Linear Equations are solved by Gaussian Elimination in Linear Algebra ...

[ajb]

So standard form is simply the expression in its most basic form...

 

In a sense, but note as I have defined it not all lines can be expressed in this way.

[Xerxes]

[math]Ax + By = C[/math],

 

with A and B both nonzero, A, B, and C are integers whose greatest common factor is 1, and A is nonnegative.

 

hello wikipedia This is a verbatim and unattributed quote (note the incorrect "nonnegative" vs the correct "non-negative" in both)

[ajb]

hello wikipedia This is a verbatim and unattributed quote (note the incorrect "nonnegative" vs the correct "non-negative" in both)

 

 

Sure you can find this definition via Wikipedia. However, you will also find the same definition all over the web and textbooks.

 

You will find "nonnegative" and "non-negative" both in use. (I have no idea which one should be considered "correct", and then things evolve, see coordinate Vs Co-ordinate)

 

So, your point is?

[Xerxes]

Sure you can find this definition via Wikipedia. However, you will also find the same definition all over the web and textbooks.

 

You will find "nonnegative" and "non-negative" both in use. (I have no idea which one should be considered "correct", and then things evolve, see coordinate Vs Co-ordinate)

 

So, your point is?

My point is, or rather was, that I had had a very "belittling" day, and wanted to appear superior to someone. Anyone. In short I was being an arsehole.

 

I apologize for the implication of mindless plagiarism. I truly do, try to forgive me

[ajb]

My point is, or rather was, that I had had a very "belittling" day, and wanted to appear superior to someone. Anyone. In short I was being an arsehole.

 

I apologize for the implication of mindless plagiarism. I truly do, try to forgive me

 

Sure, of course. Don't worry about it.

[the tree]

In a sense, but note as I have defined it not all lines can be expressed in this way.

Or any of the lines, depending on the system in question? Edited February 20, 2011 by the tree

[ajb]

Or any of the lines, depending on the system in question?

 

One may have coefficients A,B,C that are not all integers. For example, what about the line described by in "y=mx +c" form

 

[math]y = \sqrt{2}x +1[/math]?