Objectives Use matrices to store and represent data

Objectives § Use matrices to store and represent data. § Add and subtract matrices. § Multiply a matrix by a scalar.

What are matrices used for? § Used to store information in an organized manner. § Used to solve system of equations. § Many businesses, financial analysts, scientists, and teachers use matrices to store data. § By performing operations on matrices, you can manipulate the data to determine other beneficial information.

Matrix A matrix is any rectangular arrangement of elements in rows and columns.

Matrix

Example 1 § a)n 24 c) n 31 b) n 13 d) n 20, 4

Example 2 § 75%. Row 2 column 3, n 23 B) Describe the data in n 20, 2 Zelade got a 91% on the first quiz.

The DIMENSIONS of a matrix are the number of the rows and columns. The ELEMENTS are the numbers in the matrix. rows columns

3 x 3 (or square matrix) 1 x 4 (Also called a column matrix) 3 x 5 2 x 2 (or square matrix) 4 x 1 (Also called a row matrix)

Equal Matrices - two matrices that have the same dimensions and each pair corresponding elements are equal. If A = B, then a 11 = b 11, a 12 = b 12, a 13 = b 13, etc. *You can represent linear equations with matrices.

Example 4: Use matrices to represent the linear equations. Solution:

Example 5: Find the values for x and y * Form two linear equations. * Solve the system using substitution.

* Write as linear equations. * Combine like terms. * Solve using elimination.

3. Set each element equal and solve!

To add two matrices, they must have the same dimensions. Just add corresponding entries. a)

b) = = 7 0 7 7 4 5 5 7

To subtract two matrices, they must have the same dimensions. Just subtract corresponding entries. a)

b) = 2 -0 -4 -1 8 -3 0 -(-1) -7 -1 1 -(-4) 5 -2 3 -8 0 -7 = 2 -5 -5 5 1 -8 5 3 -7

To multiply a matrix by a SCALAR, you multiply each entry in the matrix by that scalar. a)

b) -2 -3 3 6 -5 -2(-3) -2(6) -2(-5) 6 -6 -12 10

Homework: § 4. 1 Practice and Apply Worksheet