Consider the set of vectors in R5; B where 3 1 -HHHH = -1 W4= 2...

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Consider the set of vectors in R5; B₁ where 3 1 -HHHH = -1 W4= 2 0 1 2 where 4 ,W₂ = Consider the set 21 = 5 2 1 7 3 1 22 2 1 = {w1, W2, W3, W4, W5, W6} B₂ = {21, 22, 23, 24, 25} 2 Show B₁ is a linearly dependent set. Then, demonstrate the conclusion of Theorem 1.2.2: Find a maximal linearly independent set B₁ of vectors from B₁, and show that the vectors from B₁ that are NOT in B set are contained in the span of B₁ (and hence, that span B₁ = span B₁). What is the dimension of span B₁? 23 = 1 2 1 7 2 24 = 1 0 3 2 -4 -2 4 1 , W5 = 7 11 3 = 0 1 2 3 0 4 1 1 Find all the vectors in the intersection span B₁ span B₂. Show that this is a subspace. 0 -1 2 1 Consider the set of vectors in R5; B₁ where 3 1 -HHHH = -1 W4= 2 0 1 2 where 4 ,W₂ = Consider the set 21 = 5 2 1 7 3 1 22 2 1 = {w1, W2, W3, W4, W5, W6} B₂ = {21, 22, 23, 24, 25} 2 Show B₁ is a linearly dependent set. Then, demonstrate the conclusion of Theorem 1.2.2: Find a maximal linearly independent set B₁ of vectors from B₁, and show that the vectors from B₁ that are NOT in B set are contained in the span of B₁ (and hence, that span B₁ = span B₁). What is the dimension of span B₁? 23 = 1 2 1 7 2 24 = 1 0 3 2 -4 -2 4 1 , W5 = 7 11 3 = 0 1 2 3 0 4 1 1 Find all the vectors in the intersection span B₁ span B₂. Show that this is a subspace. 0 -1 2 1