Answer
The equation of the least squares line associated with the given set of data points is $y=10x$
Work Step by Step
The matrices can be formed as:
$A=\begin{bmatrix}
1& 1 \\
2 & 1 \\\end{bmatrix} \rightarrow A^T=\begin{bmatrix}
1& 2 \\
1 & 1 \\\end{bmatrix}$
$x=\begin{bmatrix}
a \\
b \\
\end{bmatrix}$
$b=\begin{bmatrix}
10 \\
20
\end{bmatrix}$
Apply matrices to the least square solution:
$x_0=(A^TA)^{-1}A^Tb$
$=(\begin{bmatrix}
1& 2 \\
1 & 1 \\\end{bmatrix} \begin{bmatrix}
1& 1 \\
2 & 1 \\\end{bmatrix})^{-1} \begin{bmatrix}
1& 2 \\
1 & 1 \\\end{bmatrix}\begin{bmatrix}
10 \\
20
\end{bmatrix}$
$=\begin{bmatrix}
5 &3 \\
3&2
\end{bmatrix}^{-1}\begin{bmatrix}
1& 2 \\
1 & 1 \\\end{bmatrix}\begin{bmatrix}
10 \\
20
\end{bmatrix}$
$=\begin{bmatrix}
2 & -3 \\
-3& 5
\end{bmatrix}\begin{bmatrix}
1& 2 \\
1 & 1 \\\end{bmatrix}\begin{bmatrix}
10 \\
20
\end{bmatrix}$
$=\begin{bmatrix}
-1 &1 \\
2& -1
\end{bmatrix}\begin{bmatrix}
10 \\
20
\end{bmatrix}$
$=\begin{bmatrix}
10 \\
0
\end{bmatrix}$
The equation of the least squares line associated with the given set of data points is $y=10x$
