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Expressing the product Ax as a linear combination of the column vectors of

$A$= $\begin{bmatrix} 4 & 0 & -1\\ 3 & 6 & 2\\ 0 & -1 & 4 \end{bmatrix}$

$\vec{x}$=$\begin{bmatrix} -2\\ 3\\ 5 \end{bmatrix}$

I get it now. They just want me to multiply the two vectors together.

I end up with $\begin{bmatrix} -13\\\ 22\\\ 17 \end{bmatrix}$

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What is your question? –  user17762 Mar 20 '11 at 2:15
    
I just want to know if I'm doing this right or not. –  user8479 Mar 20 '11 at 2:19
    
I hope my answer helps, let me know if you are confused or would like more clarification! –  InterestedGuest Mar 20 '11 at 2:39
    
@InterestedQuest: Yes, your answered did help. Thank you. –  user8479 Mar 20 '11 at 2:43
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1 Answer 1

up vote 3 down vote accepted

I have edited your question to make sure it is understood correctly. So if I understand correctly, you have a matrix $A$ = $\begin{bmatrix} 4 & 0 & -1\\ 3 & 6 & 2\\ 0 & -1 & 4 \end{bmatrix}$ and a vector $\vec{x}$ = $\begin{bmatrix} -2\\ 3\\ 5 \end{bmatrix}$. You are trying to write the product $A$$\vec{x}$ as a linear combination of the column vectors of $A$. Now to do that, you need to perform the multiplication by its very definition: $\begin{bmatrix} 4 & 0 & -1\\ 3 & 6 & 2\\ 0 & -1 & 4 \end{bmatrix}$ $\cdot$ $\begin{bmatrix} -2\\ 3\\ 5 \end{bmatrix}$ actually means $-2$$\begin{bmatrix} 4\\ 3\\ 0 \end{bmatrix}$ $+$ $3$$\begin{bmatrix} 0\\ 6\\ -1 \end{bmatrix}$ $+$ $5$$\begin{bmatrix} -1\\ 2\\ 4 \end{bmatrix}$, which is what I believe your question is asking for.

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