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Unformatted text preview: end up with any extra vectors as row reducing zeros will only contribute a zero vector. Connecting Uniqueness
Theorem: A matrix that is non‐singular will always have a unique solution.
Why? Say we had an nxn matrix A and a vector b such that Ax=b is our solution. If it is non‐singular then it row reduces to the identity matrix. Since we proved that doing row operations does not change the solution set, our new system will be In x = bR where is = bR a vector that row reduces using the same row operations t...
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