39. Proof of W1+W2=L(W1 union W2) | Theorem on linear sum of subspaces | Vector Space

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38. Linear sum of subspaces definition and proof W1+W2 is subspace of V | vector space 38. Linear sum of subspaces definition and proof W1+W2 is subspace of V | vector space
Oxford Linear Algebra: Direct Sum of Vector Spaces Oxford Linear Algebra: Direct Sum of Vector Spaces
VECTOR SPACE/L#20(ii)/If 𝑊1 𝑎𝑛𝑑 𝑊2 be two subspaces of vector space V(F), then L(𝑊1 ∪ 𝑊2 ) = 𝑊1+ 𝑊2 VECTOR SPACE/L#20(ii)/If 𝑊1 𝑎𝑛𝑑 𝑊2 be two subspaces of vector space V(F), then L(𝑊1 ∪ 𝑊2 ) = 𝑊1+ 𝑊2
Theorem proof:w1 and w2 two subspace than w1union w2 is vector space iff w1 is in w2 or w2 is in w1 Theorem proof:w1 and w2 two subspace than w1union w2 is vector space iff w1 is in w2 or w2 is in w1
VECTOR SPACE/L#20(i)/IfW1 and W2 be two subspaces of vector spaceV(F), then the linear sum W1+W2 is VECTOR SPACE/L#20(i)/IfW1 and W2 be two subspaces of vector spaceV(F), then the linear sum W1+W2 is
If W1 & W2 are finite dimensional subspaces of V then dim(W1+W2) = Dim W1+Dim W2 - Dim(W1nW2) If W1 & W2 are finite dimensional subspaces of V then dim(W1+W2) = Dim W1+Dim W2 - Dim(W1nW2)
37. W1 union W2 is subspace if and only if w1 is subset w2 or w2 is subset of w1 | vector space 37. W1 union W2 is subspace if and only if w1 is subset w2 or w2 is subset of w1 | vector space
Subspaces and Span Subspaces and Span