Question-18

matrix

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

Answer

\(0\)

Solution

Let \(\displaystyle u\) be a solution to the system, then \(\displaystyle Au=b\).
\(\displaystyle b^{T} y=( Au)^{T} y=u^{T} A^{T} y=0\)