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Scalar multiplication preserves the relation because multiplying the equation $x_3 = x_1 + x_2$ by a scalar $c$ yields $cx_3 = cx_1 + cx_2$. This shows that the third component of the scaled vector $cx$ equals the sum of its first and second components.

Conditions: $x$ is a vector in the set satisfying $x_3 = x_1 + x_2$.; $c$ is a real scalar.; Scalar multiplication is defined componentwise.

Scalar multiplication preserves the relation because multiplying the equation $x_3 = x_1 + x_2$ by a scalar $c$ yields $cx_3 = cx_1 + cx_2$. This shows that the third component of the scaled vector $cx$ equals the sum of its first and second components.

Conditions: $x$ is a vector in the set satisfying $x_3 = x_1 + x_2$.; $c$ is a real scalar.; Scalar multiplication is defined componentwise.