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.
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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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 equivalent to the mill 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 eristence of a basis for a given finite dimension al subspace. For example,
if V is a subspace of R" of dimension d, then there exists vectors {v;}1 in V such that they form a
basis for V.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c73197a-a1ab-4a54-bbe1-e95f04f51e5c%2Feaf548c5-cfbb-4597-857d-c03187ff931c%2Fqo5k8v_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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 mill 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 eristence of a basis for a given finite dimension al subspace. For example,
if V is a subspace of R" of dimension d, then there exists vectors {v;}1 in V such that they form a
basis for V.
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