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Homework Statement
Find the general solution to the system:
[tex]ax+ by= 0[/tex]
[tex]cx+ dy= 0[/tex]
Consider the case when
[tex]ad- bc\neq 0[/tex]
The attempt at a solution
I multiplied the first equation by "c" and the second equation by "a", and then I subtracted the two equations.
I got the following matrix:
[tex]0...ad-bc...0[/tex]
[tex]ac...ad...0[/tex]
Therefore, [tex]ad\neq bc[/tex]. I got the general solution to be [tex]cx+ dy= 0[/tex] from the second row of the matrix. Is it right?
Find the general solution to the system:
[tex]ax+ by= 0[/tex]
[tex]cx+ dy= 0[/tex]
Consider the case when
[tex]ad- bc\neq 0[/tex]
The attempt at a solution
I multiplied the first equation by "c" and the second equation by "a", and then I subtracted the two equations.
I got the following matrix:
[tex]0...ad-bc...0[/tex]
[tex]ac...ad...0[/tex]
Therefore, [tex]ad\neq bc[/tex]. I got the general solution to be [tex]cx+ dy= 0[/tex] from the second row of the matrix. Is it right?