Problem 4. True or false? Justify your answers. (a) If linear system has exactly

Question

Problem 4. True or false? Justify your answers. (a) If linear system has exactly one solution, then its associated homogeneous system also has exactly one solution. (b) If its associated homogeneous system has exactly one solution, then a non-homogeneous linear system also has exactly one solution. (c) A system of 6 linear equations in 5 unknowns can have infinitely many solutions. (d) A system of 4 linear equations in 5 unknowns can have exactly one solution. (e) It is possible for a homogeneous linear system to have no solutions. (f) If you use Gauss’s method and the equation “0=0” appears, it means that it is not possible for the system to have exactly one solu

Explanation / Answer

4 A) TRUE . homogenous system will have same number of solution as linear system

B)True

C)True .for one solution number of equation ust be equal o number of unknowns

D) False it will have more than one solution

E) True. when the determinant will be equal to zero.

F) True. it will have infinitely many solution.

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