Stuck on a question in a test paper, my book touches this topic but in a different form.
Show that these equations are consistent and find their general solution:
Pretty sure I take the determinant.. of something.
Thanks
Stuck on a question in a test paper, my book touches this topic but in a different form.
Show that these equations are consistent and find their general solution:
Pretty sure I take the determinant.. of something.
Thanks
if determinant of that is than sys have unique solution ....
Edit:
1° when and if at least one of than solutions are unique and given
2° if and if at least one of than system of equations have no solutions
3° if and if than there can be :
a) all sub determinants of D are zeros, and coefficients with the unknowns are proportional there are 2 cases :
- all independent members of system are proportional with coefficient with unknowns than there are infinity of solutions
- all independent members of system are not proportional with coefficient with unknowns than there are no solutions
b) if at least one sub determinant of D are different from zero than there are infinity of solution
solve D_x, D_y and D_z as I wrote it to you up there in post #2
and you'll see
you have there
so what would you do now ?
Edit: because and there are sub determinants of D that are different from zero, so we know that for your system of equations there is solution , but there are infinity many of them
Just wrote all that and realised I have the PDF open9. The matrix A is defined by
a. {done this part just proving is singular when = 1}
b. Now consider the system of equations:
where
(i) Given that , show that these equations are consistent and find their general solution.
okay if you are to solve this using inverse matrix there is no solution because there can't be inverse matrix of the matrix A
you can't do inverse matrix if you have determinant of that matrix to be zero
well now we can go as I wrote it up there, and you'll see that there is infinity of the solutions ... meaning they are dependent... for any x you have different values for y and z for which equations have solutions ...
really don't know which (or how ) did they learned you how to approach to this type of problems ... but in general, same thing (post #2) or at least similar is with homogeneous and inhomogeneous systems of equations (which is easy to remember if you just try little to understand why and how did someone conclude there things ) than you'll be sure at least is there any solutions and what they are