Match the possible scenarios for system of linear equations in 3 variables.
$\begin{matrix} C o l u m n I & C o l u m n I I a . U n d e r d e t e r m i n e d s y s t e m & i . N o s o l u t i o n b . O v e r d e t e r m i n e d s y s t e m & i i . S i n g l e s o l u t i o n c . E x a c t l y d e t e r m i n e d s y s t e m & i i i . I n f i n i t e s o l u t i o n \end{matrix}$

a – i,ii; b-i,ii; c-ii, iii

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a – i,ii; b-i,ii; c-ii, iii

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a – i,iii; b-i,ii, iii; c-i, ii, iii

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a – iii, b-i, ii; c-i, ii, iii

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Solution

The correct option is C
a – i,iii; b-i,ii, iii; c-i, ii, iii

An Underdetermined system in 3 variable can’t have a single solution. It can either have no solution or infinite solution.

An overdetermined system can have no solution, single solution or infinite solution.

An exactly determined system can have no solution, exactly one solution or infinite solutions possible.

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Similar questions

Match the possible scenarios for system of linear equations in 3 variables.

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Match the possible scenarios for system of linear equations in 3 variables.

\begin{matrix} C o l u m n I & C o l u m n I I a . U n d e r d e t e r m i n e d s y s t e m & i . N o s o l u t i o n b . O v e r d e t e r m i n e d s y s t e m & i i . S i n g l e s o l u t i o n c . E x a c t l y d e t e r m i n e d s y s t e m & i i i . I n f i n i t e s o l u t i o n \end{matrix}

2 x - 3 y = 5

3 x + 4 y = - 1

2 x + 3 y - 5 = 0, 6 x + 9 y - 15 = 0

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