Let g1, g, . . . , gm be linear functionals on a linear space X. For

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Let g1, g, . . . , gm be linear functionals on a linear space X. For fixed numbers cj, the systems of equations
gj(x) = cj, j = 1, 2, . . . ,m
is consistent if and only if
E9 = 0 =jej = 0 Σλο

for every set of numbers λ1, λ2, . . . , λm.

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