In this video, the instructor explains why the first matrix transformation is placed on the right intead of left. He said “The reason is because the linear transformations act on the vector on the left, so you multiply matrix times vector.”
But shouldn’t it be linear transformations act on the vector on the right because earlier in the example of linear transformation, it was matrix times vector not vector times matrix?
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Dear @flyunicorn,
Good question!
In matrix multiplication:
(A⋅B)⋅x=A⋅(B⋅x)
- The matrix closest to the vector acts first.
- So the first transformation (B) is placed on the right.
- Then the second transformation (A) is applied next.
Both:
A · (B · x)and(A · B) · x
give the same result.
This is why transformations are written in reverse order during composition.
Thanks!
Girijesh
so it’s a mistake in the video to say it “on the left”?
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No.
but here the vector x is on the right not on the left. That’s why i thought it was a mistake
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Dear @flyunicorn,
Hope your doubts has been cleared, If not please let us know.
Looking forward to learning and growing together.
–
Girijesh
Keep Learning AI with DeepLearning.AI
Hi Girijesh, the question is if it’s a mistake that the instructor said the vector on the left, because my understanding is also what you showed in the matrix multiplication above, the vector is on the right. 
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Can you please provide me the link of the video with the timestamp? I’ll check it out and let you know.
–
Girijesh
Keep Learning AI with DeepLearning.AI
Sure. here is the link to the video and it’s around 3 min where you hear the instructor said …vector on the left…