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Vectors and Steinitz replacement

Choose two bases of V3(R) they should have no vectors in common and neither of them should contain multiples of the standard basis vectors e1, e2, e3.

a) Prove that they are indeed bases of V3(R)
b) Let one of your bases be A and the other B. Illustrate the steps of the Steinitz replacement theorem by converting B into A step-by-step.

Solution Summary

This provides an example of working with vectors as bases and Steinitz replacement.