Problem-16

system of equations

Question

If \(Ax = b\) has a solution and \(A^Ty = 0\), what is the value of \(y^T b\)?

Solution

  • Let \(u\) be a solution to the system, then \(Au=b\).

  • \(b^{T} y=( Au)^{T} y=u^{T} A^{T} y=0\)