1) For this problem, carefully state which axioms and results you use. a) Let a e F-{0}. Prove that the multiplicative inverse of a is unique. b) Let v, w e V. Prove that -(v + w) = -v + (-w).
1) For this problem, carefully state which axioms and results you use. a) Let a e F-{0}. Prove that the multiplicative inverse of a is unique. b) Let v, w e V. Prove that -(v + w) = -v + (-w).
1) For this problem, carefully state which axioms and results you use. a) Let a e F-{0}. Prove that the multiplicative inverse of a is unique. b) Let v, w e V. Prove that -(v + w) = -v + (-w).
Unless otherwise stated, F is a field. V , W, and X are vector spaces over F.
Transcribed Image Text:1) For this problem, carefully state which axioms and results you use.
a) Let a E F-{0}. Prove that the multiplicative inverse of a is unique.
b) Let v, w E V. Prove that – (v+ w) = -v + (-w).
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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