In the special case where C is the 1-by-1 unit matrix, this identity reduces to the Sherman–Morrison formula.In the special case when C is the identity matrix I, the matrix U in order to obtain the result using the right-hand side of the identity.The mined clay samples from the ten cites were mixed properly and a representative specimen for test from that location was produced using the cone and quartering system as recommended by the American Society of Testing Materials (ASTM). Atomic Absorption Spectrometer(AAS) was used to determine the chemical composition, while other established processes were used to determine other insulating properties like particle size distribution, specific gravity, bulk density, solid density, water absorption, apparent porosity, permeability to air, refractoriness, thermal shock resistance, modulus of rupture, linear shrinkage and thermal conductivity. where A, U, C and V all denote matrices of the correct (conformable) sizes.Specifically, A is n-by-n, U is n-by-k, C is k-by-k and V is k-by-n.
The values for modulus of rupture and thermal conductivity averaged 81 MN/m2 and 0.494 W/mo K.
The chemical analysis showed that all the samples had high percentages of silica and alumina, thereby classifying them as Alumino-silicates.
The values for specific gravity, bulk density, solid density and apparent porosity averaged 2.75, 2.04 g/cm3 , 3.18 g/cm3 , and 13% respectively and they were within the internationally accepted range.
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