- #1

Miike012

- 1,009

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^{n}, S = {(x,2x,3x,...,nx) | x is a real number}

I know that it is closed under addition, but to be closed under scalar mult...

say r is a scalar, then

Say we multiply S by -4

Then -4S = (-4x,-8x,...-4nx)

Because the problem never stated that the number infront of x should be pos or neg, all it said was that "x is a real number" so when I mult S by a number r x is still a real number... does this explain why S is closed under scalar mult? or not exactly?