[10] In each of the following cases, determine whether the given set S is a subspace...

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[10] In each of the following cases, determine whether the given set S is a subspace of R3 (if it is a subspace, give a proof; if not, show by example that one of the defining conditions fails to hold in general): (a) S = (b) S = {[2]-*|-----} € R³ x1x2 = X1X3 }; X2 X1 X2 X3 ER³x₁2x2 + x3 = 0 and x2 3x3 = ( 3=0}. [10] In each of the following cases, determine whether the given set S is a subspace of R3 (if it is a subspace, give a proof; if not, show by example that one of the defining conditions fails to hold in general): (a) S = (b) S = {[2]-*|-----} € R³ x1x2 = X1X3 }; X2 X1 X2 X3 ER³x₁2x2 + x3 = 0 and x2 3x3 = ( 3=0}.