# 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...

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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### 1 Answer

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**