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what is consistency system and inconsistency sytem in determinant?
 

Asked by akpanda729125 17th May 2016, 9:34 PM
Answered by Expert
Answer:
straight A space system space of space equations space may space have space straight a space unique space solution comma space or space many space solutions comma space or space no space solution space at space all.
If space it space has space straight a space solution space left parenthesis whether space unique space or space not right parenthesis space the space system space is space said space to space be space consistent space system.
If space it space has space no space solution comma space it space is space called space inconsistent space system.

Conditions space for space consistency space and space inconsistency space of space straight a space system space in space determinant

Case 1 space colon space For space straight a space system space of space 2 space simultaneous space linear space equations space with space 2 space unknown
left parenthesis straight i right parenthesis space If space straight D not equal to 0 comma space then space the space given space system space of space equation space is space consistent space and space has space straight a space unique space solution space given space by
straight x space equals space straight D subscript 1 over straight D comma space space straight y space equals straight D subscript 2 over straight D.
left parenthesis ii right parenthesis space If space straight D space equals space 0 space and space straight D subscript 1 equals straight D subscript 2 space equals space 0 comma space then space the space system space is space consistent space and space has space infinitely space many space solutions.
left parenthesis iii right parenthesis space If space straight D space equals space 0 space and space one space of space the space space straight D subscript 1 space and space straight D subscript 2 space space is space nonzero comma space then space the space system space is space inconsistent.


Case 2 space colon space For space straight a space system space of space 3 space simultaneous space linear space equations space with space 3 space unknown
left parenthesis straight i right parenthesis space If space straight D not equal to 0 comma space then space the space given space system space of space equation space is space consistent space and space has space straight a space unique space solution space given space by
straight x space equals space straight D subscript 1 over straight D comma space space straight y space equals straight D subscript 2 over straight D comma space and space space straight z space equals straight D subscript 3 over straight D
left parenthesis ii right parenthesis space If space straight D space equals space 0 space and space straight D subscript 1 equals straight D subscript 2 space equals straight D subscript 3 space equals space 0 comma space then space the space system space of space equations space may space or space may space not space be space consistent. space However comma space if space it space is space consistent comma space then space it space has space infinitely space many space solutions.
left parenthesis iii right parenthesis space If space straight D space equals space 0 space and space at space least space one space of space the space space straight D subscript 1 comma space straight D subscript 2 comma space straight D subscript 3 space space is space non minus zero comma space then space the space system space is space inconsistent.
Answered by Expert 18th May 2016, 10:59 AM
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