Product of a Matrix by a Scalar

Product of a Matrix by a Scalar

The product of a matrix A by a scalar k, written kA or Ak, is the matrix of the same format as A obtained by multiplying all the elements of A by k.

Example

Consider the matrix A = $$\begin{pmatrix} 3 & 6 & 7\\4 & 8 & 5\end{pmatrix}$$.

Then: $$4\begin{pmatrix} 3 & 6 & 7\\4 & 8 & 5\end{pmatrix}=\begin{pmatrix} 12 & 24 & 28\\16 & 32 & 20\end{pmatrix}$$.