Lienar Algebra please show all work, Question 4. Consider the follow.pdf

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Lienar Algebra please show all work, Question 4. Consider the following statement and proof we did in class: Proposition. Let V be a vector space over a field F. Then for z epsilon V, we have - 1F . x = -x Proof. Solution 1)0F x=-0 x=0v 2) (1+(-1))x= 1x+(-1x)=x-x=0v 3)1.x+(-1.x)=x-x=0v 4)x+(-1.x)=x-x=0v 5)-x+x+(-1.x)=-x+x-x=-x+0v 6)0v+(-1.x)=0v-x=-x+0v 7)-1.x+0v=-x+0v 8)-1.x=-x.

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