Are the following following maps <, >: V × VR inner products? Verify the inner product axioms. 1. V = R², < (x1,y1), (x2, y2) >= x1x2 - Y1Y2 2. V = R², < (x1,y1), (x2, y2) >= x1Y2+ Y1x2 3. VMn(R) all n x n matrices. < A, B >= det(AB) 4. V = R³, < (x1, Y1, Z1), (x2, Y2, Z2) >= (x1 y1 21) 0 • 1 0 0 0 020 X2 Y2 The map is a multipli- 0 0 1 22 cation of matrices.

Are the following following maps <, >: V × VR inner products? Verify the inner product axioms. 1. V = R², < (x1,y1), (x2, y2) >= x1x2 - Y1Y2 2. V = R², < (x1,y1), (x2, y2) >= x1Y2+ Y1x2 3. VMn(R) all n x n matrices. < A, B >= det(AB) 4. V = R³, < (x1, Y1, Z1), (x2, Y2, Z2) >= (x1 y1 21) 0 • 1 0 0 0 020 X2 Y2 The map is a multipli- 0 0 1 22 cation of matrices.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.3: Systems Of Inequalities

Problem 24E

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