Given $a_1,a_2,\gamma,b_1,b_1 \in\mathbb{R}$.
Say if the Linear Least Squares problem of the following matrix has solution and if yes how many? $$ A= \begin{bmatrix} a_1 & \gamma a_1 \\ a_2 & \gamma a_1\\ \end{bmatrix} $$ $$ b= \begin{bmatrix} b_1 \\ b_2 \end{bmatrix} $$
My answer is this: "According to one of the theorems if $A \in \mathbb{C}^{m\times n}$ and its range is maximum then its linear least squares problem has one solution and it is $A^*AX= A^*b$"
Now using the above theorem I said the problem of the least linear squares of the given matrix has unique solution since $\det(A)= \gamma a_1^2-\gamma a_1a_2 \neq 0$.
Is my solution correct? or should i have semplifed the above equation?
Thank you!