(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose A is a fixed matrix in M. Apply the subspace theorem to show that

S = {x[itex]\in[/itex] ℝ : Ax=0}

3. The attempt at a solution

Zero vector forx= <0,0,0>

A*<0,0,0> = 0

Therefore zero vector is in ℝ and S is non-empty.

Addition:

Foru&v[itex]\in[/itex] S

u+v=0+0= 0

A*(u+v) =0=> A(0) = 0

S is closed under addition

Multiplication:

λ [itex]\in[/itex] R

λ*A*u= λ*0= 0

Therefore closed under multiplication and by subspace theorem, if a subspace of S.

Is this correct?

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# Subspace theorem problem (matrix)

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