Answer:
No, scientist can't be certain that, if the right sides of the equations are changed, the new non homogeneous system will have a solution.
Step-by-step explanation:
Consider the system [tex]Ax=b[/tex].
Where A is given matrix
A non homogeneous system of ten linear equations in twelve unknowns and finds that three of the unknowns are free variables.
Here the given matrix is a 10×12 matrix.
It is given that three of the unknown are free variable, that means the dimension of null A is 3.
The rank of the matrix is:
[tex]rank\ A=n-dimNul\ A\\12-3=9[/tex]
Since, the rank of the matrix is 9 and there are 10 equations that means the system cannot have a solution for all "b".
Therefore, the system [tex]Ax=b[/tex] is inconsistent.
No, scientist can't be certain.
No, the scientist can't be sure that if the right sides of the equations are changed, the new nonhomogeneous system will have a solution.
According to the task content, the nonhomogeneous system of equations is linear in twelve unknowns with three variables being free.
On this note, it is noteworthy to know that the free variables are due to the insufficient number of equations. The equation will therefore not have a solution until three other equations are added.
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