Basis maths-linear algebra-Q11

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A system of linear equations with fewer equations than unknowns is sometimes called an underdetermined system. Such a system will Never be

(A) consistent having a unique solution

(B) consistent having infinitely many solutions

(C) Inconsistent having no solution

(D) None

asked May 15 in Basic Maths by gbeditor (44,500 points)
reshown May 16 by gbeditor

1 Answer

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An underdetermined system always has more variables than equations. There cannot be more basic variables than there are equations, so there must be at least one free variable. Such a variable may be assigned infinitely many different values. If the system is consistent, each different value of a free variable will produce a different solution.
answered May 16 by deepak-gatebook (112,390 points)