The product of a matrix with a vector is a linear image. The multiplication is explained if the number of columns of the matrix is equal to the number of elements of the vector. The result is a vector whose number of components equals the number of rows of the matrix. This means that a matrix with 2 rows always maps a vector to a vector with two components.

$A\cdot \overrightarrow{v}=\left(\begin{array}{cccc}{a}_{11}& {a}_{12}& \dots & {a}_{1m}\\ {a}_{21}& {a}_{22}& \dots & {a}_{2m}\\ & \vdots \\ {a}_{n1}& {a}_{n2}& \dots & {a}_{nm}\end{array}\right)\cdot \left(\begin{array}{c}{v}_{1}\\ {v}_{2}\\ \vdots \\ {v}_{m}\end{array}\right)=\left(\begin{array}{c}{a}_{11}{v}_{1}+{a}_{12}{v}_{2}+\dots +{a}_{1m}{v}_{\mathrm{m}}\\ {a}_{21}{v}_{1}+{a}_{22}{v}_{2}+\dots +{a}_{2m}{v}_{\mathrm{m}}\\ \vdots \\ {a}_{n1}{v}_{1}+{a}_{n2}{v}_{2}+\dots +{a}_{nm}{v}_{\mathrm{m}}\end{array}\right)$

Input of the matrix elements: a_{11}, a_{12}, ... and the vector elements, v_{1}, v_{2}, ...

Multiplication of the matrix with the vector:

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