Hello,
Kindly look at the image below:
DOUBT:
Why is the coordinates not matching up in the later transformation?
[[1, 1], [-2, 1]] and [[1], [2]] should be [[3], [0]] as so on.
What am I doing wrong here?
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Hi @Debatreyo_Roy!
Thanks for noticing this. There is indeed an error in the slide.
The resulting matrix,
\left[ \begin{array}{cc} 1 & 4 \\ -3 & 3 \end{array}\right]
Is incorrect given the situation described. I will explain why.
Let’s give letters to things. Let’s call T_1: P_1 \rightarrow P_2 the first linear transofmation that takes the first parallelogram and transforms it into the second and let T_2: P_2 \rightarrow P_3 the second linear transformation.
So the vectors that are the edges of the first parallelograms, say v will go through the following schema:
P_1 \longrightarrow P_2 \longrightarrow P_3
x \longrightarrow T_1(x) \longrightarrow T_2(T_1(x))
So, the resulting matrix is T_2 \cdot T_1 = \left[ \begin{array}{cc} 4 & 3 \\ -5 & 0 \end{array}\right] and not T_1 \cdot T_2 = \left[ \begin{array}{cc} 1 & 4 \\ -3 & 3 \end{array}\right] .
When looking at composing linear transformations (in fact, this happens with every composing function) we should swap the orders, because of the diagram above.
I will send it to our video team to fix it as soon as possible.
Regards,
Lucas
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Thank you for the detailed clarification. 
I thought my understanding of the previous classes were incorrect.