Artificial intelligent assistant

Using data from Hooke's law to model a force vector associated with displacement I have this practice exam question, I know the answer to it, but I'm not sure why the answer is what it is. I went to my school's tutoring center, but none of them are well versed in linear algebra so they weren't of any help. The answer to this is C, and I've tried working backwards without success. So my question is, why is the solution C? ![enter image description here](

It is just a question of identifying what are $y_i$ and $u_i$. The force $y_i$ is proportional to the applied mass (3rd column in the table). The displacement $u_i$ is the amount the spring is extended **from the equilibrium position**. The equilibrium position is when the force (mass) is $0$. That means looking at the second column and subtracting $0.140$ from the current position. Let's call our matrix $M$, with elements $M_{ij}$, with $i$ from $1$ to $5$ and $j=1$ or $j=2$. When we do the matrix-vector multiplication, we can write $y_1=M_{1,1}b+M_{1,2}k$. We know that $y_1=b+k u_1= b+k 0$. This means $M_{1,1}=1$ and $M_{1,2}=0$. At this point, the possible answers are B. or C. If you write the same equations for the second term you get $M_{2,1}b+M_{2,2}k=b+0.051k$, so the answer is C.

xcX3v84RxoQ-4GxG32940ukFUIEgYdPy 648836c557685b604609e7edde769095