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Thursday, July 27, 2017

Advanced Knowledge Problem of the Week: Is the vector in the span? [Linear Algebra]

Be sure to let us know how you solved this in the comments below or on social media!

Solution below.




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  2. That the Simplex Algorithm (pivoting) revises the scalars on the “Tableau of Detached Coefficients” in the way one computes them with matrix-vector algebra is verified by experience only! The revision formula for i \neq i{0}

    \bar{a_{i, j}} = ( a_{i, j}a_{i_{0}, j_{0}} - a_{i, j_{0}}a_{i_{0}, j} ) / a_{i_{0}, j_{0}}

    with pivot a_{i_{0}, j_{0}} is not written in any textbook as if it is unnecessary. A “Fundamental Theorem of Simplex Algorithm” is due to be proven. Am I right?