Question

"matrix multiplication" please respond to the following: determine whether or not matrix multiplication is commutative. support your answer using at least one (1) real-world example of scenario.

Answer 1

Answer:

Matrix multiplication is not commutative.

Step-by-step explanation:

Matrix multiplication is not commutative which means that the result of A*B is not equal to the result of B*A which suggests that the order does matter in matrix multiplication.

AB ≠ BA

Real-world Example:

We can model a set of equations that will represent the number of games  won by each team.

Let x represents team Brazil and y represents team Spain.

2x + 3y = 12

6x + 8y = 34

In the matrix form

$\left[\begin{array}{ccc}2&3\\6&8\\\end{array}\right]$   $\left[\begin{array}{ccc}x\\y\\\end{array}\right]$   $= \left[\begin{array}{ccc}12\\34\\\end{array}\right]$

When we solve this matrix we get x = 3 and and y = 2

Which means that Brazil has won 3 games and Spain has won 2 games.

Now if you change the order of these variables then you wont get the correct results and this is exactly why matrix multiplication is not commutative because the order is important in matrix multiplication.