hi HallsofIvy and Modilion,

I've contacted the author since and the following is the snippet from his response that I'd like to share.
Hope it clarifies any doubts ..

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The x in Eq. 12 & 13 is just matrix multiplication and is there because the equation continued onto a second line. I understand how these little things can be so difficult to those starting who need the information the most.
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thanks you.

--islahna