Matrix (Matrices)- Is a rectangular array of real numbers

   _        _

   |  a   b  | 

   |_c   d _|

*To add Matrices, you just add the numbers that are in exactly the same spots.

 ___  ___           _          _

| -5     0    |    +  |6       -3  |

|_4__  1 _|        |_2      _3 |

Solution

    - 1      -3

      6       4

    *When subtracting, you do the same thing as you do as adding.

Matrices

A Matrix is an array of numbers:

A Matrix

(This one has 2 Rows and 3 Columns)

We talk about one matrix, or several matrices.

There are many things we can do with them ...

Adding

To add two matrices: add the numbers in the matching positions:

These are the calculations:

The two matrices must be the same size, i.e. the rows must match in size, and the columns must match in size.

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 match in size)

Negative

The negative of a matrix is also simple:

These are the calculations:

Subtracting

To subtract two matrices: subtract the numbers in the matching positions:

These are the calculations:

Note: subtracting is actually defined as the addition of a negative matrix: A + (-B)

Multiply by a Constant

We can multiply a matrix by some value:

These are the calculations:

We call the constant a scalar, so officially this is called "scalar multiplication".

even and odd functions