# Matrices Problem

Let A=$\begin{pmatrix} -1 & 2 & -3 \\ -5 & 3 & -3 \\ -3 & 2 & -2 \end{pmatrix}$ and B=$\begin{pmatrix} 0 & -2 & 3 \\ -1 & -7 & 12 \\ -1 & -4 & 7 \end{pmatrix}$ Find AB, if possible.

I am very confused about matrices in general, I understand systems of linear equations but once they became matrices it stopped making sense. Looking for a full detailed answer, I would like to learn how to do this kind of problem!

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• Sorry, I have never heard of a dot product. Could you explain that please?

• Say you want to multiply the first row of the first matrix by the first column of the second matrix (color coded in green). Then you can write both as column vectors and do a dot product: (-1, 2, -3). (0,-1,-1)=-1*0+2*(-1)+(-3)*(-1)=1.

• This is how the dot product is defined: (a,b,c).(x,y,z)=ax+by+cz. Indeed you simply multiply the corresponding terms and add.

• Look at my multiplications and see how those numbers are multiplied, everything will be clear in a minute.