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Examine if the set is subspace of R3 s = {(x, y, z) € R3 : x= 0} |
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Answer» Let \(V_1, V_2 \in S\) such that \(V_1 = (x_1, y_1, z_1) \) & \(V_2 = (x_2, y_2, z_2) \) then x1 = 0 and x2 = 0. Let \(a \in R\) Now, \(aV_1 + V_2 = ax_1,y_1, z_1) + (x_2,y_2,z_2)\) \(= (ax_1 + x_2, ay_1+y_2, az_1+ z_2)\in S\) \((\because ax_1 + x_2 = a\times 0 + 0 = 0)\) \(\therefore\) S is subspace of \(R^3\). |
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