Describing ppt on Non - Homogeneous Linear System

Ppt on Non - Homogeneous Linear System

3. TypesofLinearSystem
A)Non-homogeneouslinearsystem:Alinearsystemissaidtobenonhomogeneouslinearsystemif
AX=BwhereBisnonzeromatrix.
Fore.g.
1)5x+7y=352)
2x-3y=6
B)HomogeneousLinearSystem:AlinearsystemissaidtobehomogeneouslinearsystemifAX=B
whereBisZeromatrixornullmatrix.
Fore.g.
1)4x-5y=0
2)8x+3y=0

4. AugmentedMatrix
Anaugmentedmatriisamatrixformedbycombiningthecolumnsoftwomatricestoformanewmatrix.
Theaugmentedmatrixisanimportanttoolinmatricesusedtosolvesimplelinearequations.Thenumber
ofrowsintheaugmentedmatrixisequaltothenumberofvariablesinthelinearequation.

5. TypesofNonhomogeneouslinearsystem
1.ConsistentSystem
Thesystemisconsistentifp(A)=p(A|B)
A)ifp(A)=p(A|B)=No.ofVariablesthensystemhasuniquesolutions.
B)ifp(A)=p(A|B)<No.ofVariablesthensystemhasinfinitesolutions.
2.InconsistentSystem
Thesystemisinconsistentifp(A)≠p(A|B)andithasnosolution.

6. KeypointsofNon-Homogeneoussystems
Anonhomogeneoussystemhasnosolutionsiflinesareparallelordoesnot
intersect.
Anonhomogeneoussystemhasonesolutioniftwolinesintersecteachother.
Anonhomogeneoussystemhasinfinitesolutioniftwolinesareoverlapping
eachother.

7. ExampleofNonHomogeneousLinear
System
1)x-y+2z=2,2x+y+4z=7,4x-y+z=4

9. 2)2x+2y+z=5,x-y+z=1,3x+y+2z=4

11. 3)x+y+z=3,x+2y+3z=4,x+4y+9z=6
2z=0
x=2,y=1,z=0

12. Non-homogeneouslinearsystemcontainsconstantterm,uniquesolution,linear
combinationandmatrixoperations.
Thesecanbeusedinengineering,physics,economics,computerscienceandetc.