Unit 1.8 – Perform Basic Matrix Operations

Unit 1 – Algebra: Linear Systems, Matrices, & Vertex- Edge Graphs  1.8 – Perform Basic Matrix Operations  Georgia Performance Standard:  MM3A4a  Add, subtract, multiply, and invert matrices, when possible, choosing appropriate methods, including technology.  MM3A4c  Examine the properties of matrices, contrasting them with properties of real numbers

Vocabulary/Need to Know  A matrix is a rectangular arrangement of numbers in rows and columns.  The dimensions of a matrix with m rows and n columns are m x n.  The numbers in a matrix are its elements.  Equal matrices have the same dimensions and the elements in corresponding positions are equal.

Vocabulary/Need to Know  To add or subtract two matrices, simply add or subtract elements in corresponding positions.  You can add or subtract matrices only if they have the same dimensions.  In matrix algebra, a real number is often called a scalar.  To perform scalar multiplication you multiply each element in the matrix by the scalar.

Properties of Operations  Associative Property of Addition (A+B) +C= A +(B+C)  Commutative Property of Addition A +B = B + A  Distributive Property of Addition K(A+B) = KA + KB  Distributive Property of Subtraction K(A-B) = KA - KB

How Can I tell what are rows and Columns? Rows – Left to Right Columns – Up and Down

How do I write dimensions? Rows x Columns

What are the dimensions?

Add and Subtract Matrices  To add or subtract matrices, the dimensions have to be EXACTLY the same.

Try these…  Guided Practice:  Page 38: 1-4

Multiplying Matrices with a Scalar  When multiplying by a scalar, you have to distribute throughout the entire matrix!

Try this one…

Solve a multi-step problem  Last year you planted 12 geraniums, 36 begonias, and 20 petunias. This year you planted 10 geraniums, 40 begonias, and 32 petunias. Organize the data using two matrices. Write and interpret a matrix that gives the average number of flowers for the two year period.

Matrix Equations