Matrix - Scalar Multiplication

Scalar multiplication of a matrix involves multiplying every element of the matrix by a single number, known as a scalar.

To multiply a matrix $A$ by a scalar $k$, you simply multiply each entry of the matrix by $k$. For example, if we have the matrix:

$$A=\left(\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\end{array}\right)$$

and we want to multiply it by the scalar $k=3$, the resulting matrix $B=kA$ is calculated as follows:

$$B=3\left(\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\end{array}\right)=\left(\begin{array}{ccc}3\cdot 1& 3\cdot 2& 3\cdot 3\\ 3\cdot 4& 3\cdot 5& 3\cdot 6\end{array}\right)=\left(\begin{array}{ccc}3& 6& 9\\ 12& 15& 18\end{array}\right)$$