This may seem an odd and complicated way of multiplying, but it is necessary! I can give you a real-life example to illustrate why we multiply matrices in this way.

Example: a matrix with 3 rows and 5 columns can be added to another matrix of 3 rows and 5 columns. But it could not be added to a matrix with 3 rows and 4 columns (the columns don't …

When we multiply a matrix by its inverse we get the Identity Matrix (which is like "1" for matrices):

OK, to multiply two vectors it makes sense to multiply their lengths together but only when they point in the same direction. So we make one "point in the same direction" as the other by …

Multiplying Complex Numbers The Complex Plane Common Number Sets Inequalities "Equal To" is nice but not always available. Maybe we only know that something is less than, or greater …

We went on to solve it using "elimination", but we can also solve it using Matrices! Using Matrices makes life easier because we can use a computer program (such as the Matrix Calculator) to …

The rows and columns are all swapped over (transposed), and the order of multiplication is reversed, but it still works. Just so you know.

☐ Know the conditions under which two matrices can be multiplied, and how to perform the multiplication.

Introduction to Matrices Types of Matrix How to Multiply Matrices Determinant of a Matrix Inverse of a Matrix: Using Elementary Row Operations (Gauss-Jordan) Using Minors, Cofactors and …

Notice how we multiply a matrix by a vector and get the same result as when we multiply a scalar (just a number) by that vector. How do we find these eigen things?