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):

Enter your matrix in the cells below "A" or "B". Or you can type in the big output area and press "to A" or "to B" (the calculator will try its best to interpret your data).

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 …

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

Associative Laws The "Associative Laws" say that it doesn't matter how we group the numbers (i.e. which we calculate first) ... ... when we add: (a + b) + c = a + (b + c) ... or when we …

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 pattern continues for larger matrices: multiply a by the determinant of the matrix that is not in a 's row or column, continue like this across the whole row, but remember the + − + − pattern.

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?