An exactly determined system always has solutions.

True

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False

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Solution

The correct option is B
False

No. An exactly determined system can have no solution, single solution or infinite solutions.For example,

$\begin{matrix} x + y + z = 3 x + y + z = 2 x + y + z = 1 \end{matrix} ⎫ ⎪ ⎬ ⎪ ⎭ n o s o l u t i o n \begin{matrix} x + 0. y + 0. z = 0 0. x + y + 0. z = 0 0. x + 0. y + z = 0 \end{matrix} ⎫ ⎪ ⎬ ⎪ ⎭ i n f i n i t e s o l u t i o n$

Therefore given statement is false

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