4.2 adding and subtracting matrices 4.3 matrix multiplication date: _____________
TRANSCRIPT
4.2Adding and Subtracting Matrices
4.3Matrix Multiplication
Date: _____________
Adding and Subtracting Matrices
• Must be the same dimensions
• Add or Subtract corresponding elements
Adding MatricesTo add matrices, add all the corresponding elements.
4 -27 0 +
3 25 -3 =
7 012 -3
Subtracting MatricesTo subtract matrices, subtract all the corresponding elements.
4 -27 0 −
3 25 -3 =
1 -42 3
12-413-7
-8192314
− =
20-23-10-21
129-3
− =0-2 4
7
Not Possible!
Dimensions are not the same.
Solving a Matrix Equation
1 0 10 7
2 5 4 4X
Get the variable by itselfThe variable is representing a matrix
1 0
2 5
1 0
2 5
11 7
6 1X
Subtracting matrices
Solving a Matrix Equation1 2 5 6
2 1 1 0
3 4 8 5
X
1 2
2 1
3 4
X
Subtracting matrices1 2
2 1
3 4
4 -8-
1-11
11
4 8
1 1
11 1
X
1
2 5 4 25 4
3 3 12 3 18
x
y y
Solving Equation MatricesEach corresponding element is equal
2 5 25x 3 12 18y y 5 5
2 30x 2 2
15x
12 12y y
2 6y 2 2
3y
Muliplying MatricesScalar Multiplication – multiply a matrix by a factor.
15 12 10 0320 10 7 0
Same concept as the Distributive Property
45 -36 30 060 -30 21 0
Matrix Multiplication
m x n p x q
If n = p, multiplication is possible.
If multiplication is possible, the answer will have dimensions m x q.
Suppose that you want to multiply matricesA and B. A has dimensions m x n and B has dimensions p x q.
2 97 8
5 82 3
2 x 2 2 x 2
multiplication is possible.
answer will be 2 x 2
(2)(5) + (9)(2) (2)(8) + (9)(3)
(7)(5) + (8)(2) (7)(8) + (8)(3)=
28 4351 80
FUN?
DON’T FORGET YOUR CALCULATOR!!!