Chapter 9 Matrices

Chapter 9 Matrices

 Matrix is a Rectangular arrangement of numbers.

For example:

This matrix has 2 rows (Vertical) and 3 columns (Horizontal). 

Types of matrices
Diagonal matrices: A matrix with non-zero entries only on the diagonal
                               
Upper triangular: A diagonal matrix whose non-zero entries are all 1's
                               
Identity matrices: A matrix with all-zero entries below the top-left-to-lower-right diagonal
                               

There are a number of basic operations that can be applied to matrices, it's called matrix addition, scalar multiplication, transposition, matrix multiplication, row operations, and submatrix.

Addition & Subtracting: to add two matrices, add the numbers in the matching positions.

How its done?
3+4=7                                                8+0=8
4+1=5                                                6+(-9)=-3

How it's done?
3-4=-1                                                8-0=8
4-1=3                                                  6-(-9)=15

In addition and subtracting, the  two matrices must be the same size, meaning the rows and the columns of the matrices should be the same size.

Multiply
   -By a whole number

          How it's done?
               2 * 4=8                       2 * 0=0
               2 * 1=2                       2 * (-9)= -18

   -By another matrices

         How it's done?
                  (1 * 7)+(2 * 9)+(3 * 11)=58 (top left)
                  (1 * 8)+(2 * 10)+(3 * 12)=54 (top right)
                  (4 * 7)+(5 * 9)+(6 * 11)=139 (bottom left)
                  (4 * 8)+(5 * 10)+(6 * 12)=154 (bottom right)