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In: Advanced Math

For each of the subspaces ? and ? of ?4 (ℝ) defined below, find bases for...

For each of the subspaces ? and ? of ?4 (ℝ) defined below, find bases for ? + ? and ? ∩ ?, and verify that dim[?] + dim[? ] = dim[? + ? ] + dim[? ∩ ? ]

(a) ? = {(1, 3, 0, 1), (1, −2, 2, −2)}, ? = {(1, 0, −1, 0), (2, 1, 2, −1)}

(b) ? = {(1, 0, 1, 2), (1, 1, 0, 1)}, ? = {(0, 2, 1, 1), (2, 0, −1, 0)}

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Colby Messinger answered 1 year ago
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