Properties of matrix scalar multiplication  Matrices
Properties of matrix scalar multiplication
Lessons
Notes:
Note
Let $X,Y$ be matrices with equal dimensions, and $c$ and $d$ be scalars. Then we have the following scalar
multiplication properties:
Dimension property for scalar multiplication
The matrix $c \cdot X$ has the same dimensions as $X$.
Associative property
$c \cdot X=X \cdot c$
$c \cdot (dX)=d \cdot (cX)=(dc)X$
Distributive property
$c(X+Y)=cX+cY$
$(c+d)X=cX+dX$
There are also some scalar multiplication properties with the zero matrix
Multiplication property for the zero matrix
$0 \cdot X=O$
$c \cdot O=O$

2.
Let . Show that the following is true:

3.
You are given that , , $c=5$ and $d=3$. Show that:

c)
$(c+d)(X+Y)=c(X+Y)+d(X+Y)$