# Explicit linear combination of some matrices

I apologize in advance for how messy this is, I've never had to use latex.

\begin{matrix} 10 \\ 40 \\ 30 \\ 20 \end{matrix}

This is matrix A

\begin{matrix} 1 \\ 2\\ 3\\ 4\\ \end{matrix}

This is matrix B

\begin{matrix} 1 \\ 1\\ 1\\ 1\\ \end{matrix} This is matrix C

\begin{matrix} -9 \\ 17\\ -7\\ -1\\ \end{matrix}

This is matrix D

How does $A*4(B)*-15(C)=D$ ?

It's an example in my notes that I need to know, and for the life of me I can't figure it out. For more context:

$y_i=\alpha x_i+\beta+\epsilon_i$ for a regression chart, with matrix B being the x values and matrix A being the y values. Matrix D is the values of the $\epsilon$ values. How do we arrive at $\epsilon$?

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Take a look at this answer – Pragabhava Oct 25 '12 at 3:26

What you actually seem to have is $A=4B+15C+D$ except for a transposition in $A$. Perhaps you meant $A-4B-15C=D$?

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Oh that's exactly what it is! Thank you very much, it makes perfect sense too. – Unknown Oct 25 '12 at 3:29