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 \(Au=b\).
\(b^{T} y=( Au)^{T} y=u^{T} A^{T} y=0\)
If \(Ax = b\) has a solution and \(A^Ty = 0\), what is the value of \(y^T b\)?
Let \(u\) be a solution to the system, then \(Au=b\).
\(b^{T} y=( Au)^{T} y=u^{T} A^{T} y=0\)