1
$\begingroup$

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).

  • 0
    You're welcome. It's been fun. And thanks for satisfying my curiosity.2010-11-11

1 Answers 1

1

Solution exists iff $b$ is orthogonal to the null space of $A^{*}$. This is typically referred to as the Fundamental Theorem of Linear Algebra.

  • 1
    @ Mark: The dual to the above is $b^{*}z = 0$ subject to $A^{*}z = 0$2010-11-10