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Math · Advanced Math
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One of the most difficult skills to learn and master in Mathematin convincing proof. To help introduce you to this skill. through the proof Exercises in this and in fit I1. Suppose that i (3, 1,-4) is translated so that its head is at (-1,2, 3). Where is its tail? 12. Suppose that P - (8,-3,6) and 0 (4, 1,-2). Find u PO. For Exercises (13) to (20): You will be asked to prove some general statements about vector operations. Be sure you know the definitions for the operations involved, and use proper notation for the vectors. You should also state which of the Field Axioms for Real Numbers from Chapter Zero is applied to some steps: 13. Prove the Closure Property for Vector Addition and for Scalar Multiplication: For all vectors u, v E R, and all scalars r E R:計급 E R and ru E R. 14. Prove the Commutative Property for Vector Addition: For all vectors , V e Rutv+u. 15. Prove the Associative Property for Vector Addition: For all vectors it, , WE R: 16. Prove the Right Distributive Property of Vector Arithmetic: For all vectors i, VeR and scalars r e R:r (u+)-rutr.v. 17. Prove the Associative Properhy of Scalar Muliplication: For all vectonsi c R and sealarsr, 18. Prove that for any scalar k e IR and any vector iW e R3: WIkI. 13 please
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