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Multiplication of a matrix by a number

To multiply a matrix by a number we multiply all the entries of the matrix by this number. This number is often called a scalar.

$$$ \Tred{2}\begin{pmatrix}1&2\\-1&0\end{pmatrix} = \begin{pmatrix}\Tred{2}\times 1&\Tred{2}\times 2\\\Tred{2}\times -1&\Tred{2}\times 0\end{pmatrix} = \begin{pmatrix}2&4\\-2&0\end{pmatrix} $$$