I'm super stuck. I have a severe brain injury but I'm trying really hard to get my degree. Please be gentle! Question is attached.
I guess I'm kind of stuck between not knowing what the question is asking me to confirm and where to start. I know it involves a sort of reverse engineering to find out what row operations have been used. When I see the $ta$, $rb$ and $sa$ thrown in, I get lost. What do those even mean?
Can someone help?
Confirm the following identity without evaluating the determinant directly:
$$\begin{vmatrix} a_1& b_1+ta_1& b_1+rb_1+sa_1\\ a_2& b_2+ta_2& c_2+rb_2+sa_2\\ a_3& b_3+ta_3& c_3+rb_3+sa_3 \end{vmatrix}=\begin{vmatrix} a_1&a_2 &a_3 \\ b_1&b_2 &b_3 \\ c_1&c_2 &c_3 \end{vmatrix}$$