MATRICES

1
MATRICES

• Danny Nguyen
• Marissa Lally
• Clauberte Louis

• HOW TO'S
• ADD, SUBTRACT, AND MULTIPLY MATRICES.

2
Subtracting Matrices

• The dimensions of a matrix refer to the number of
  rows and columns of a given matrix.
• of rows x of columns
• The subtraction of matrices is only allowed if
  matrices are the SAME size!!
• If the matrix doesn't have the same of rows and
  columns you cannot subtract them.

3
FORBIDDEN!!
-3 5
ERROR!
4 -7

• You CANNOT subtract 1 x 2 matrix and a 2 x 1
  matrix!
• They are NOT the same size
• You can't just flip the second matrix to make it
  the same either!

4
CORRECT!
WHAT?!
2 -5 1 7 10 -1
1 2 3 4 5 6
1-2 2-(-5) 3-1 4-7 5-10 6-(-1)
-1 7 2 -3 -5 7
5
0 1 2 6 5 4 9 8 7
3 4 5
HOW TO SOLVE?
Both or more matrices must have the same
dimensions to be able to add, if not, the
operation cannot be done.
(0 6) (1 5) (2 4) (9 3) (8 4) (7 5)
6 6 6 12 12 12
ADDING MATRICES
For example, you cannot add a 2x3 matrix with a
3x2 matrix.
0 2 4 5 7 5 4 5 2 1
ERROR!
6
Multiplying matrices (property) To multiply an
mn matrix by an np matrix, the ns must be the
same, and the result is an
mp matrix.

• Associative property
• A (BC) (AB) C
• Example
• 4 x (3 x 2) 24 or (2 x 4) x 3 24
• Left distributive property
• A (B C) AB AC
• Example
• 2 x (3 4) 23 24

• Associative property (scalar)
• C(AB)(cA)BA(cB)
• Example
• 3 x (2 x 5) (3 x 2) x 5 2 x (3 x 5)
• Right distributive property
• (A B) C AC BC
• Example
• (23) x4 2x 4 3 x 4

7
Multiplying matrices ( scalars)

• Explanation If you are multiply a matrix by a
  scalar you have to multiply each entry in the
  matrix by the scalar.
• Example
  

• We call the number ("2" in this case) a scalar,
  so this is called
• "scalar multiplication".

• calculations

248 200
212 2-9-18
8

• Multiplying matrices
• (dot product)

• Explanation When multiply a 1 n matrix by an
  n 1 matrix, you want to know the first row is a
  single row and the second is a single column. You
  want to name the rows and then the column. Then
  the product of the row and column is formed. (1
  1 matrix)

• you want to do 1st row by 1st column.

( 1, 2, 3) (7, 9, 11) 17 29 311 58
you want to do 1st row by 2nd column

• (1, 2, 3) (8, 10, 12) 18 210 312 64

DONE!!