(Solved): For this exercise, you may use the Matrix Multiplier Calculator below to assist you in answering th ...

For this exercise, you may use the Matrix Multiplier Calculator below to assist you in answering the questions. Matrix Multiplier Input Matrix values Select Matrix Operation: \( A B \bigcirc B A \quad A^{T} A \bigcirc A A^{T} \bigcirc A^{-1} B A \quad O A B A^{-1} O A^{-1} \) \( \left[\begin{array}{ll}1 & 5 \\ 0 & 1\end{array}\right] \) The following system is inconsistent. \[ \begin{array}{r} 5 x_{1}+3 x_{2}-3 \\ 5 x_{1}+3 x_{2}--1 \\ 2 x_{1}+x_{2}-1 \end{array} \] We denote this inconsistent system as \( A \dot{x}=\vec{b} \). Determine the vector \( \vec{x} \) that minimizes the Euclidean distance \( \|\vec{b}-A \vec{x}\| \).