Show that V is not a vector space over R under the (x,y) +(z,t)= (0,y+t) and α(x,y)= (αx, αy)

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Show that V is not a vector space over R under (x,y) +(z,t)= (x+z,y+t) and α(x,y)= (0, αy) Show that V is not a vector space over R under (x,y) +(z,t)= (x+z,y+t) and α(x,y)= (0, αy)
Show that V is not a vector space over R under (x,y) +(z,t)= (x+z,y+t) and α(x,y)= (αx, y) Show that V is not a vector space over R under (x,y) +(z,t)= (x+z,y+t) and α(x,y)= (αx, y)
Show that V is not a vector space over R under the (x,y) +(z,t)= (x+z,y+t) and α(x,y)= (α²x, α²y) Show that V is not a vector space over R under the (x,y) +(z,t)= (x+z,y+t) and α(x,y)= (α²x, α²y)
Lesson 4: General properties of vector space [ α(-x) = - (αx ) = (-α)x ∀ α∈ F and x ∈ V ] Lesson 4: General properties of vector space [ α(-x) = - (αx ) = (-α)x ∀ α∈ F and x ∈ V ]
V={(x,y)}Show V is not vector space defined(x,y)+(z,t)=(x+z,y+t)and alpha(x,y)=(alpha^2x,alpha^2y) V={(x,y)}Show V is not vector space defined(x,y)+(z,t)=(x+z,y+t)and alpha(x,y)=(alpha^2x,alpha^2y)
Understanding Vector Spaces Understanding Vector Spaces
A non-empty subset W of vector space is subspace of V iff αx+βy ∈ W for all α,β∈F and x,y∈W A non-empty subset W of vector space is subspace of V iff αx+βy ∈ W for all α,β∈F and x,y∈W
Lesson 3: General properties of vector space i) α.0 = 0 ∀ α∈F ii)0.x = 0 ∀ x∈V Lesson 3: General properties of vector space i) α.0 = 0 ∀ α∈F ii)0.x = 0 ∀ x∈V