# Math Help - Simple matrices question

1. ## Simple matrices question

So I was wondering, if you have a matrix such as
A=2(2 5 6
......4 3 2
......7 4 8)
(ignore the dots)
it is equilvalent to B=(4 10 12
.............................8 6 4
.............................14 8 16)
??
Does the 2 in front mean that it is multiplied in. If not, what does it stand for?
Thanks!

2. Originally Posted by sberxa
So I was wondering, if you have a matrix such as
A=2(2 5 6
......4 3 2
......7 4 8)
(ignore the dots)
it is equilvalent to B=(4 10 12
.............................8 6 4
.............................14 8 16)
??
Does the 2 in front mean that it is multiplied in. If not, what does it stand for?
Thanks!
Yes, they are equivalent. When you multiply a matrix by a scalar, you multiply each element in the matrix by that scalar value:

$2\begin{bmatrix}2&5&6\\4&3&2\\7&4&8\end{bmatrix}=\ begin{bmatrix}2\cdot{\color{red}2}&5\cdot{\color{r ed}2}&6\cdot{\color{red}2}\\4\cdot{\color{red}2}&3 \cdot{\color{red}2}&2\cdot{\color{red}2}\\7\cdot{\ color{red}2}&4\cdot{\color{red}2}&8\cdot{\color{re d}2}\end{bmatrix}=\begin{bmatrix}4&10&13\\8&8&4\\1 4&8&16\end{bmatrix}$

--Chris