Matrices

A matrix is an ordered set of numbers placed in a square/rectangular shape. 

You read the dimensions of a matrix by telling how many rows there are by number of columns. The example below is a 3x4 matrix.

                                                                                                                                                                        [ 1 2 3 4 ]

                                                                                                                                                                        [ 2 6 7 8 ]

                                                                                                                                                                        [ 3 0 1 2 ]

Different Types of Matrices:

Square Matrix: Has same number of rows as column: [ a b ]

                                                                                [ c d ]

Diagonal Matrix: Every number in a square matrix is zero, besides the diagonal ones: [ 1 0 0 ]

                                                                                                                              [ 0 1 0 ]

                                                                                                                              [ 0 0 1 ]

Row Matrix: One row matrix [21 3 5]

Column Matrix: One column matrix: [4]

                                                       [3]

                                                       [1]

The Identity Matrix: Multiplying a matrix with its identity matrix helps determine the inverse of the original matrix. If you get the original numbers after multiplying, there is an inverse. If you don't, there is no inverse. 

What Can You Do With Matrices?

Addition and Subtraction: 

    Solution: Just add the corresponding numbers. 

                  Just make sure both of the matrices are the same size, meaning having the same number of rows and columns.

                  Subtraction works the exact same way, just subtract instead of add, obviously.

Multiply:  *2

    Solution: Multiply each number in the matrix by two. DISTRIBUTE!

Solve AB:

When multiplying matrices, you need to know the dimensions. In this example, the dimensions are 2x3 and 3x2. The two middle numbers have to be the same. In this case, they are (both 3's). This tells you that you can multiply these matrices. The outside numbers (2 and 2) tell you what the dimensions will be for your product. Then you take the first row of matrix A and multiply it with matrix B's first column. You multiply until the row and column is finished then add them all together for the first entry of the new matrix.

ALWAYS REMEMBER: MULTIPLY THEN ADD! & THE DIMENSIONS NEED TO BE THE SAME AND ORDER MATTERS!

Determinant of Matrices:

For information about finding Determinants of Matrices and the importance of a Determinant. http://www.mathsisfun.com/algebra/matrix-determinant.html