9 1. If W is a subspace of R" and if v is in both W and W+, then v must be the zero vector. 9 2. The Gram-Schmidt process produces from a linearly independent set {x1,...,X, } an orthogonal set {v1,..., v,} with the property that for each k, the vectors vị,..., Vg span the same subspace as tha ned by X,..., Xg- * 3. For any scalar c, and vectors u, v e R", we have u · (cv) = c(u · v). 4. If x is not in a subspace W, then x - projw (x) is zero. 5. For all vectors u, v E R", we have u· V = -V .u.

9 1. If W is a subspace of R" and if v is in both W and W+, then v must be the zero vector. 9 2. The Gram-Schmidt process produces from a linearly independent set {x1,...,X, } an orthogonal set {v1,..., v,} with the property that for each k, the vectors vị,..., Vg span the same subspace as tha ned by X,..., Xg- * 3. For any scalar c, and vectors u, v e R", we have u · (cv) = c(u · v). 4. If x is not in a subspace W, then x - projw (x) is zero. 5. For all vectors u, v E R", we have u· V = -V .u.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.6: Rank Of A Matrix And Systems Of Linear Equations

Problem 67E: Let A be an mn matrix where mn whose rank is r. a What is the largest value r can be? b How many...

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