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u1 = (1,2,3), u2 = (0,1,2), u3 = (2,0,1) generate R3(R).

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Vector Space and Subspaces
Euclidian 3-space

Problem:- Show that the vectors u1 = (1,2,3), u2 = (0,1,2), u3 = (2,0,1) generate R3(R).

https://brainmass.com/math/linear-algebra/generating-linear-algebra-12327

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LINEAR ALGEBRA

Vector Space and Subspaces

Problem:- Show that the vectors
u1 = (1,2,3), u2 = (0,1,2), u3 = (2,0,1)
generate R3(R).

Solution:-Here R3(R) is a vector space called Euclidian 3-space.

Let (a,b,c) Ð„ R3 be an arbitrary vector .
If (a,b,c) Ð„ R3 is a linear combination of the vectors
u1 = ...

Solution Summary

This solution is comprised of a detailed explanation for finding the vector space and subspaces. It contains a step-by-step explanation to show that the vectors u1 = (1,2,3), u2 = (0,1,2), u3 = (2,0,1) generate R3(R).

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