2.3 Scalar Multiplication

The product of an m × n matrix A and a scalar α\alpha is an m × n matrix whose elements are the arithmetic products of α\alpha and the elements of A.

𝐂=α𝐀\mathbf{C}=\alpha\cdot\mathbf{A} (7)

implies

cij=αaij,where1imand1jnc_{ij}=\alpha\cdot{a}_{ij},\operatorname{where}1\leq i\leq m\operatorname{and}% 1\leq j\leq n (8)