# Thread: Multiplying matrices what is W?

1. ## Multiplying matrices what is W?

What is W in BWS = 3, where B = [4 9 -3 9] and S = [2 5 -1 0]. Note that S matrix is written vertically but I can't write it here.

Is it not possible because B would have to be vertical to multiply with B, but then S is vertical and you can't multiply that with a vertical W? Or am I totally confused?

2. Originally Posted by brumby_3
What is W in BWS = 3, where B = [4 9 -3 9] and S = [2 5 -1 0]. Note that S matrix is written vertically but I can't write it here.

Is it not possible because B would have to be vertical to multiply with B, but then S is vertical and you can't multiply that with a vertical W? Or am I totally confused?
thanks Soroban , time to revise my matrix

3. So I got 56 for BS. I can't figure out W though.

4. Hello, brumby_31

Marix multiplication is not commutative!
. . You cannot multiply out-of-order.

What is $\displaystyle W$ in $\displaystyle BWS = 3$,

where $\displaystyle B \:=\:\begin{bmatrix}4 & 9 & \text{-}3& 9\end{bmatrix}\,\text{ and }\,S \:=\:\begin{bmatrix}2\\5\\\text{-}1\\0\end{bmatrix}$

$\displaystyle B\text{ is }1\times 4,\,\text{ and }\,S\text{ is }4\times 1 \quad\rightarrow\quad W\text{ is }4\times 4.$

The equaton has this form: .$\displaystyle \begin{bmatrix}4&9&\text{-}3&9\end{bmatrix}\,\begin{bmatrix}a&b&c&d \\ e&f&g&h \\ i&j&k&l \\ m&n&p&q\end{bmatrix}\,\begin{bmatrix}2\\5\\\text {-}1\\0\end{bmatrix} \;=\;\begin{bmatrix}3\end{bmatrix}$

We have 16 unknowns and (basically) one equation.

Good luck!