3. Let W be a subspace of R" of dimension k

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3 Let W Be A Subspace Of R Of Dimension K N Use The Fundamental Theorem Of Linear Algebra To Prove That W Is Equivale 1 (36 KiB) Viewed 55 times

3. Let W be a subspace of R" of dimension k<n. Use the Fundamental Theorem of Linear Algebra to prove that W is equivalent to the null space of some matrix. Note that this implies that W is an intersection of hyperplanes in R” that also intersect the origin. Hint: You may assume the existence of a basis for a given finite dimensional subspace. For example, if V is a subspace of Rm of dimension d, then there exists vectors {vi}in V such that they form a basis for V.