Question

An undetermined set of linear equations is always inconsistent.

• A. True
• B. False

Answer 1

The correct option is B

False

An undetermined system can be either be consistent or inconsistent. For example consider the set linear equations, {x + 2y + 3z = 4, x + 2y + 3z = 5} and {2x + y + z = 2, 2x + y + 3z = 1}.

In $1^{st}$case there are no solutions possible because if there exists an (x,y,z) which satisfies x +2y+3z=4 then it cannot satisfy x +2y+3z=5.

In $2^{nd}$ case let’s put z = k then 2x+y=2-k and 2x+y =1-3k $\to$ which will give k = $\frac{-1}{2}$. Therefore for z = $\frac{-1}{2}$ we have infinite values of (x,y) for x +2y = $\frac{5}{2}$. Therefore infinite solutions which is a consistent case.