**a weighted sum of observations.**

**Example**

Consider a table of students' grades, as shown below.Now, suppose we want to find the final grade for each student. We can do this by multiplying the matrix by a vector of weights, where figures represent the percentage of each component that contributes to the final grade. For example, if we Define the weights for each component

- final_weight = 0.5
- mid_weight = 0.25
- homework_weight = 0.15
- attendance_weight = 0.10

90*0.5+ 80*0.25+90*0.15+100*0.1 = 88.5

When you multiply a matrix and a vector of weights, you get a new matrix with one row for each student. Each row in the new matrix represents the student's final grade under a different grade scheme.

Suppose we want to know which grading scheme will produce the highest class average. We can use matlab to run average calculation. It turns out the third one gives us the best class performance.

This is just one example of how matrix multiplication can be used to find a weighted sum of observations.

Matrix multiplication is a powerful tool that can be used to solve a variety of problems. For example, it can be used to solve systems of linear equations. By understanding how it works, you can use it to make sense of complex data and to solve problems that would be difficult to solve with other methods.

**Another way - linear **transformation

**Reference**

https://www.mathworks.com/learn/training/matlab-fundamentals.html