(Solved): (10 pts) Task 3: An overdetermined system \( A x=b \) is a linear system of equations that has more ...

(10 pts) Task 3: An overdetermined system \( A x=b \) is a linear system of equations that has more equations than unknown variables. However, there is in general no exact solution to an overdetermined system. Instead, we look for the least-squares solution \( x \) with the smallest 2 norm error such that \( \|A x-b\|^{2} \). The following presents an overdetermined system, 1 \[ \left\{\begin{array}{l} c+2 d=1 \\ c+\frac{3}{2} d=2 \\ c+4 d=1 \end{array}\right. \] Please find its least squares solution \( \left[\begin{array}{l}c \\ d\end{array}\right] \). (Hint: Slide 42 and Slide 47 of Topic 3.3)