Linear Combination and Span
Consider the vector space R2 over R. If(x, y) = α(2,3) and α = -4, then find the value of (x, y)
Let W be a subspace of a vector space R3 over R. For x, y, z ∈ W, which of the following is true?
Let S be a subspace of a vector space over R. For S={0}, K ≡ {αx+βy: x, y ∈ S and α, β ∈ R} equals
Consider the vector R2 over R. Let
(i) (4, 8)=α(2, 3) for some αϵR
(ii) (2, 3)=α(1, 1)+β(-1, -1) for some α, β ϵ R
Then which of the following is true
(i) (4, 8)=α(2, 3) for some αϵR
(ii) (2, 3)=α(1, 1)+β(-1, -1) for some α, β ϵ R
Then which of the following is true
(-4, 12) = α(-2, 0) + β(0, 6) if α and β equals to