MATA23H3 Lecture : Subspace, basis, rank
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Example: if a is an m n matrix and n is the nullspace of a, then n is a subspace of. Example: if w = sp(v1, v2, , vm) where v1, v2, vm rn, then w is a subspace of rn. www. notesolution. com. Example: if w = { [x1, x2, x3, x4] r4(cid:12)(cid:12)(cid:12) a subspace of r4. x1 = x3 x4, x2 = x3 + x4 }, determine if w is. Example: is w = { [x1, x2, x3] r3(cid:12)(cid:12)(cid:12) x1 + x3 = x2 + 3 } a subspace of r3? www. notesolution. com. The plural for the word basis is bases . W is a subspace of r4. a basis for w ? www. notesolution. com. Theorem: b = {b1, b2, , bk} be a basis for the subspace w of rn if and only if. B = {b1, b2, , bk} is a linearly independent set of vectors and w = sp(b1, b2, , bk) www. notesolution. com.
