In each case study below, the number of degrees of freedom in the gas composition (G, with G + 1 the number of components in the gas) is greater than the number of MOFs (M ) comprising the sensor (array). Thus, (i) the sensor's mapping under a from gas composition space to sensor response space is non-injective and (ii) the inverse problem to determine the gas composition from the sensor response is underdetermined. Accordingly, the sensor (array) will contain a non-trivial unresponsive subspace.