suppose that x1=-1; x2=2; x3=4; x4=-3 is a solution of a nonhomogeneous linear system Ax=b and that the solution set of the homogeneous system Ax=0 given by the formulas x1=-3r+4s; x2=r-s; x3=r; x4=s.
a) Find a vector form of the general solution of Ax =o
b) Find a vector form of the general solution of Ax =b
Anyone helps me, please

Question

suppose that x1=-1; x2=2; x3=4; x4=-3 is a solution of a nonhomogeneous linear system Ax=b and that the solution set of the homogeneous system Ax=0 given by the formulas x1=-3r+4s; x2=r-s; x3=r; x4=s.
a) Find a vector form of the general solution of Ax =o
b) Find a vector form of the general solution of Ax =b
Anyone helps me, please

sirm3d · Answer

the vector form of the general solution to the homogeneous system AX = 0 is $$\left[\begin{matrix}-3r+4s\r-s\r\s\end{matrix}\right]=r\left[\begin{matrix}-3\1\1\0\end{matrix}\right]+s\left[\begin{matrix}4\-1\0\1\end{matrix}\right]$$

anonymous · Answer

yes. thanks a lot. I got it. don't we have to form A? from those solution of x to get b and then get b)

sirm3d · Answer

i am thinking of this, but i don't know yet how to proceed. i'm not even sure if this is the right approach.$$AX=B \Rightarrow AX = 0 + B$$