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

[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.

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

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 ...

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.

[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)

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?

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

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.

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, 201114 yr by the tree

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]?