Matrix calculator for the multiplication of a matrix with a vector

Multiplication of a vector with a matrix

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.

$A\cdot \overrightarrow{v}=\left(\begin{array}{cccc}{a}_{11}& a_{12}& \dots & a_{1m}\\ a_{21}& a_{22}& \dots & a_{2m}\\ & ⋮\\ a_{n1}& a_{n2}& \dots & a_{nm}\end{array}\right)\cdot \left(\begin{array}{c}{v}_1\\ v_2\\ ⋮\\ v_m\end{array}\right)=\left(\begin{array}{c}{a}_{11}{v}_1+a_{12}{v}_2+\dots +a_{1m}{v}_{\mathrm{m}}\\ a_{21}{v}_1+a_{22}{v}_2+\dots +a_{2m}{v}_{\mathrm{m}}\\ ⋮\\ a_{n1}{v}_1+a_{n2}{v}_2+\dots +a_{nm}{v}_{\mathrm{m}}\end{array}\right)$

Calculator for the product of Matrix A with Vector v

Number of rows=

Number of columns=

↹#.000

Input of the matrix elements: a₁₁, a₁₂, ... and the vector elements, v₁, v₂, ...

Multiplication of the matrix with the vector:

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