1123581321 Posted February 19, 2011 Share Posted February 19, 2011 I was wondering what exactly 'standard form' is/means in the area of linear equations Link to comment Share on other sites More sharing options...
ajb Posted February 19, 2011 Share Posted February 19, 2011 [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. Link to comment Share on other sites More sharing options...
1123581321 Posted February 19, 2011 Author Share Posted February 19, 2011 So standard form is simply the expression in its most basic form... Link to comment Share on other sites More sharing options...
khaled Posted February 19, 2011 Share Posted February 19, 2011 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 ... Link to comment Share on other sites More sharing options...
ajb Posted February 19, 2011 Share Posted February 19, 2011 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. Link to comment Share on other sites More sharing options...
Xerxes Posted February 19, 2011 Share Posted February 19, 2011 [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) Link to comment Share on other sites More sharing options...
ajb Posted February 19, 2011 Share Posted February 19, 2011 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? Link to comment Share on other sites More sharing options...
Xerxes Posted February 20, 2011 Share Posted February 20, 2011 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 2 Link to comment Share on other sites More sharing options...
ajb Posted February 20, 2011 Share Posted February 20, 2011 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. Link to comment Share on other sites More sharing options...
the tree Posted February 20, 2011 Share Posted February 20, 2011 (edited) 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 Link to comment Share on other sites More sharing options...
ajb Posted February 20, 2011 Share Posted February 20, 2011 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]? Link to comment Share on other sites More sharing options...
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