# Compute the product AB by the definition of the product of​ matrices, where Ab_1 text{ and } Ab_2 are computed​ separately, and by the​ row-column rule for computing AB. A=begin{bmatrix}-1 & 2 2 & 55&-3 end{bmatrix} , B=begin{bmatrix}4 & -1 -2 & 4 end{bmatrix} Determine the product AB AB=?

Compute the product AB by the definition of the product of​ matrices, where are computed​ separately, and by the​ row-column rule for computing AB.
$A=\left[\begin{array}{cc}-1& 2\\ 2& 5\\ 5& -3\end{array}\right],B=\left[\begin{array}{cc}4& -1\\ -2& 4\end{array}\right]$
Determine the product AB
AB=?
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Step 1
$A=\left[\begin{array}{cc}-1& 2\\ 2& 5\\ 5& -3\end{array}\right],B=\left[\begin{array}{cc}4& -1\\ -2& 4\end{array}\right]$
$A=\left[\begin{array}{cc}-1& 2\\ 2& 5\\ 5& -3\end{array}\right],B=\left[\begin{array}{cc}4& -1\\ -2& 4\end{array}\right]$
$A{b}_{1}=\left[\begin{array}{c}\left(-1\right)\cdot 4-2\cdot 2\\ 2\cdot 4-2\cdot 5\\ 5\cdot 4+3\cdot 2\end{array}\right]=\left[\begin{array}{c}-8\\ -2\\ 26\end{array}\right]$
$A{b}_{2}=\left[\begin{array}{c}\left(-1\right)\left(-1\right)+2\cdot 4\\ 2\left(-1\right)+4\cdot 5\\ 5\left(-1\right)-3\cdot 4\end{array}\right]=\left[\begin{array}{c}9\\ 18\\ -17\end{array}\right]$
Jeffrey Jordon