Matrix Multiplication with a Scalar

1. Multiplying a Scalar Value with a Matrix involves Multiplying all the Elements of the Matrix with that Scalar Value.
2. Given a \(M \times N\) Matrix \(A\) as following
   
   \(A=\begin{bmatrix} a_{11} & a_{12} & ... & a_{1n}\\ a_{21} & a_{22} & ... & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\a_{m1} & a_{m2} & ... & a_{mn}\end{bmatrix}\)
   
   Multiplying Matrix \(A\) with a Scalar Constant \(k\) gives
   
   \(kA= ka_{ij}=\begin{bmatrix} ka_{11} & ka_{12} & ... & ka_{1n}\\ ka_{21} & ka_{22} & ... & ka_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ka_{m1} & ka_{m2} & ... & ka_{mn}\end{bmatrix}\)