Find a necessary and sufficient condition for the linear equation Ax = b to have no solution. (hint: Use duality to find a strong alternative to Ax = b).
Use duality to find a strong alternative
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linear-programming
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0You're welcome. It's been fun. And thanks for satisfying my curiosity. – 2010-11-11
1 Answers
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Solution exists iff $b$ is orthogonal to the null space of $A^{*}$. This is typically referred to as the Fundamental Theorem of Linear Algebra.
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1@ Mark: The dual to the above is $b^{*}z = 0$ subject to $A^{*}z = 0$ – 2010-11-10