How to multiply matrix with row vector?

  • #1
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How do I calculate a 3x3 matrix multiplication with a 3 column row vector, like below?

##
\begin{bmatrix}
A11 & A12 & A13\\
A21 & A22 & A23\\
A31 & A32 & A33
\end{bmatrix}\begin{bmatrix}
B1 & B2 & B3
\end{bmatrix}
##
 
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Answers and Replies

  • #2
You can only multiply matrix times column or row times matrix.
$$
\begin{pmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{pmatrix}\cdot
\begin{pmatrix}b_{1}\\b_{2}\\b_{3}\end{pmatrix}=
\begin{pmatrix}a_{11}b_{1}+a_{12}b_{2}+a_{13}b_{3}\\a_{21}b_{1}+a_{22}b_{2}+a_{23}b_{3}\\a_{31}b_{1}+a_{32}b_{2}+a_{33}b_{3}\end{pmatrix}
$$
 
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