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Let V, < ·, · > be inner product vector spaces. Let S C V be some collection of vectors. Let S be the set of all vector in V that are orthongonal to all vectors in S. Show that S- is a subspace. Verify that the following is an inner product on R². < (x1, x2), (Y1, Y2) >= x1Y1 - x1Y2 - x2Y1 + 3x2Y2 Find a vector orthogonal to (1,5) with respect to this new inner product. Find a vector orthogonal to (1,5) with respect to this standard inner product.

Let V, < ·, · > be inner product vector spaces. Let S C V be some collection of vectors. Let S be the set of all vector in V that are orthongonal to all vectors in S. Show that S- is a subspace. Verify that the following is an inner product on R². < (x1, x2), (Y1, Y2) >= x1Y1 - x1Y2 - x2Y1 + 3x2Y2 Find a vector orthogonal to (1,5) with respect to this new inner product. Find a vector orthogonal to (1,5) with respect to this standard inner product.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.1: Introduction To Linear Transformations
Problem 78E: Let S={v1,v2,v3} be a set of linearly independent vectors in R3. Find a linear transformation T from...
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Let V, < ·, · > be inner product vector spaces. Let S C V be some collection of vectors. Let S be the set of all vector in V that are orthongonal to all vectors in S. Show that S- is a subspace.
Transcribed Image Text:Let V, < ·, · > be inner product vector spaces. Let S C V be some collection of vectors. Let S be the set of all vector in V that are orthongonal to all vectors in S. Show that S- is a subspace.
Verify that the following is an inner product on R². < (x1, x2), (Y1, Y2) >= x1Y1 - x1Y2 - x2Y1 + 3x2Y2 Find a vector orthogonal to (1,5) with respect to this new inner product. Find a vector orthogonal to (1,5) with respect to this standard inner product.
Transcribed Image Text:Verify that the following is an inner product on R². < (x1, x2), (Y1, Y2) >= x1Y1 - x1Y2 - x2Y1 + 3x2Y2 Find a vector orthogonal to (1,5) with respect to this new inner product. Find a vector orthogonal to (1,5) with respect to this standard inner product.
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