Matrices for the stupid

A good friend of mine has been trying to explain Matrices to me as a mathematical tool. His description of the function and rules was wonderful but I couldn’t get my head around the applications in the real world. I’m a bit of a dunce in this department. So I went hunting and found the most basic example I could to explain the use of Matrices to the layman. – Deskarati

Let’s say we want to find the final grades for 3 girls, and we know what their averages are for tests, projects, homework, and quizzes.  We also know that tests are 40% of the grade, projects 15%, homework 25%, and quizzes 20%.

Here’s the data we have:

School Grades Data

Let’s organize the following data into two matrices, and perform matrix multiplication to find the final grades for Alexandra, Megan, and Brittney.  To do this, you have to multiply in the following way:

Matrix Multiplication of Grades

Just remember when you put matrices together with matrix multiplication, the columns (what you see across) on the first matrix have to correspond to the rows down on the second matrix. You should end up with entries that correspond with the entries of each row in the first matrix.

For example, with the problem above, the columns of the first matrix each had something to do with Tests, Projects, Homework, and Quizzes (grades).  The row down on the second matrix each had something to do with the same four items (weights of grades).  But then we ended up with information on the three girls (rows down on the first matrix).

So Alexandra has a 90, Megan has a 77, and Brittney has an 87.  See how cool this is?   Matrices are really useful for a lot of applications in “real life”! Via shelovesmath

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