Guided Proof Prove that if is orthogonal to each vector in then is orthogonal to every
Chapter 5, Problem 64(choose chapter or problem)
Guided Proof Prove that if is orthogonal to each vector in then is orthogonal to every linear combination of vectors in Getting Started: To prove that is orthogonal to every linear combination of vectors in you need to show that their dot product is 0. (i) Write as a linear combination of vectors, with arbitrary scalars in S. (ii) Form the inner product of w and v. (iii) Use the properties of inner products to rewrite the inner product as a linear combination of the inner products (iv) Use the fact that w is orthogonal to each vector in to lead to the conclusion that w is orthogonal to
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