Matrices

Matrices

1. a matrix is a rectangular array of numbers

   • includes columns and rows
   • each matrix has an order, which is m x n (row x columns)

2. Multiplying matrices

   • to multiply matrices, the number of columns in the first must equal the number of rows in the second
     • n in the first must equal m in the second
   • Scalor multiplication
     • works like expanding brackets
   • multiplying two matrices
     • 1. first in row of A x first in column of B
     • 2. second in row of A x second in column of B
     • 3. product of step 1 + product of step 2
     • 4. this creates the first row of the product matrix
   • multiplying bigger matrices
     • 1. same as steps 1-3 of normal multiplication
     • 2. do steps 1-3 for the first row and second column
     • 3. Do steps 1-3 for second row and first column
     • 4. Do steps 1-3 for second row and second column

3. special matrices

   • identity matrix
     • 1's make a diagonal line from the top left corner
   • zero matrix
     • all subjects are 0's
     • whatever you multiply the zero matrix by, you always get the zero matrix