Matrices: lines addition master trick.

[MadAtom]

In Jordan, Gauss-Jordan and Laplace it's necessary to miltiply a line by a constant, add the result to other line in order to obtain 'zeros' (to facilitate the process while using Laplace) or to obtain a identity matrix (Jordan and Gauss-Jordan).

I take TOO long while doing this and sometimes never acomplish. Is there some magic trick for this, a logic algorithm I should follow or I can only get better with practice?

 

[rock.freak667]

All of the elements in the diagonal of the identity matrix are 1 with all the other elements being zero. So in your initial matrix, in the first row, you would use the first element to make the rest of elements within that first column 0.

Similarly then you go to the second row and use the second element to make the rest of elements in the 2nd column 0.

It is easier to see an example here.

 

[LCKurtz]

In Jordan, Gauss-Jordan and Laplace it's necessary to miltiply a line by a constant, add the result to other line in order to obtain 'zeros' (to facilitate the process while using Laplace) or to obtain a identity matrix (Jordan and Gauss-Jordan).

I take TOO long while doing this and sometimes never acomplish. Is there some magic trick for this, a logic algorithm I should follow or I can only get better with practice?

No, there is no magic trick. It is inherently a tedious and error-prone procedure. What is important is to understand the nature of what you are doing. Once you understand, you could perhaps use a computer algebra program to do it for you.

 

[MadAtom]

All of the elements in the diagonal of the identity matrix are 1 with all the other elements being zero. So in your initial matrix, in the first row, you would use the first element to make the rest of elements within that first column 0.

Similarly then you go to the second row and use the second element to make the rest of elements in the 2nd column 0.

It is easier to see an example here.

Thank you! I didn't notice that before... Very helpful.