If the coefficient matrix A in a homogeneous system of 22 equations in 16 unknowns is known to have rank 5, how many free parameters are there in the general solution? This question pertains to linear systems

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That the coefficient matrix A has rank five implies that there are five linearly independent solutions to the system of 22 equations. Therefore, 5 of the 16 unknowns are dependent parameters and the remaining 11 are independent or free parameters.

The general solution then consists of 5 equations expressing the 5 dependent unknown parameters as linear combinations of the 11 independent parameters.

There are 11 free parameters in the general solution

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