1. 2.3 Modeling Real World Data with Matrices
Objectives: Model data using matrices. Add, subtract, and multiply matrices.

2. A rectangular array of terms called elements.
In a matrix they are m x n
A matrix with m rows and n columns. “m by n”
A matrix with only one row.
A matrix with only one column.
A matrix with the same number of rows as columns.
Matrix: Dimensions: m x n matrix: Row matrix: Column matrix: Square matrix:

3. a23 is the element in
the second row and
third column.
a a12 a13 a14
a21 a22 a23 a24
a31 a32 a33 a34
a41 a42 a43 a44

4. Ex. 1
During the summer of 2000, Ms. Robbins received several types of grains on her farm to feed her livestock.
a.) Use a matrix to represent the data.
June – 15,000 bushels of corn
- 2,000 bushels of soybeans
- 500 bushels of oats
July – 13,500 bushels of corn
- 6,500 bushels of soybeans
- 1,000 bushels of oats
Aug ,000 bushels of corn
- 5,500 bushels of soybeans
bushels of oats.
b) Use a symbol to represent the number of bushels of soybeans in August.

5. Equal Matrices:
Two matrices are equal iff they have the same dimensions and are identical, element by element.
Ex. 2)
Find the values of x and y for which the matrix equation is: y x
y – x + 1
The sum of two m x n matrices is an m x n matrix in which the elements are the sum of the corresponding elements of the given matrices.
Addition of Matrices:

6. Subtraction of Matrices:
Ex. 3)
Find A + B if A= and B =
The difference A – B of two m x n matrices is equal to the sum of A + (-B), where –B represents the additive inverse of B.
Subtraction of Matrices:
Find S - T if S = and T =
Ex. 4)

7. Scalar:
The number multiplied by a matrix.
Scalar Product:
The product of a scalar k and an m x n matrix A is an m x n matrix denoted by kA. Each element of kA equals k times the corresponding element of A.
Ex. 5)
If A = Find 4A

8. Product of Two Matrices:
The product of an m x n matrix A and an n x r matrix B is an m x r matrix AB. The ijth element of AB is the sum of the products of the corresponding elements in the ith row of A and the jth column of B.
*Can only multiply if the number of columns in A is the same as the number of rows in B.
Product of Two Matrices:

9. Use matrices A = 4 -1 2 0 1 0 3 -2 4 B = 4 2 C = 1 2 -3 -2 3 3 1 0 AB
Ex. 6.)
Use matrices A =
B = C = AB
b.) BC