Showing that two vector spaces are equal.

Thread starter jdinatale
Start date Jan 20, 2013
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Vector Vector spaces

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To show that two vector spaces are equal, containment in both directions is necessary. The user has successfully established containment in one direction but struggles with the reverse. They propose using specific linear combinations of vectors to express the relationship. The challenge lies in solving for the original vectors in terms of the new ones. Finding a solution for the ##v_i## in terms of the ##w_i## is crucial for completing the proof of equality between the vector spaces.

Jan 20, 2013

jdinatale

I thought that I should do containment in both directions. I have containment in one direction, but the other is much harder. Any ideas?

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Jan 20, 2013

LCKurtz

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Call ##w_1= v_1,\ w_2 = c_{12}v_1+v_2,\ w_3 = c_{13}v_1+c_{23}v_2 + v_3## Can you solve for the ##v_i## in terms of the ##w_i##?

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