Using Matrices to Solve Systems of Equations Honors Algebra II with Trigonometry Mrs. Stacey

Essential Stuff: Essential Questions: Essential Vocabulary How do you use matrices to solve systems of equations? How do you find the determinants of 2x2 and 3x3 matrices? Essential Vocabulary Matrices Determinant Cramer’s Rule

Terminology Matrix: A rectangular array of numbers written within brackets. A = Matrix Element: Each term of the matrix is called an element. Name element by row and column. Explain that this is called a 2x3 matrix. ((ROW x Column)) On the board name each matrix element. EX: a11=-1 a12=7 a13=-1 a21=6 a22=2 a23=3

Matrices Matrices: Allow us to organize and manipulate data. Can also be used to solve systems. Augmented Matrices Organize data: Brothers Sisters Student 1: Student 2: **Make a 3x2 matrix** Student 3:

Terminology Square Matrix: A matrix with the same number of rows & columns. Examples of square matrices: 4x4 Matrix 2x2 Matrix

Determinants Square matrices have a special value called the determinant. The determinant will help us find the solution to systems of equations.

Determinants A = detA = ad – bc To find the determinant of a 2 x 2 matrix, you find the difference of the diagonals, starting with the main diagonal. Determinant of a 2 x 2 matrix… detA = ad – bc A =

There are three ways to represent the determinant of a matrix: Determinants Evaluate the determinant of matrix A. There are three ways to represent the determinant of a matrix:

Determinants We can also find determinants using our calculators. Examples…

Inverses A square matrix A will have an Inverse, also known as 𝑨 −𝟏 if the detA ≠0.

To find the inverse of a 2x2 matrix use the following formula: 𝑤ℎ𝑒𝑛 𝐴= 𝑎 𝑏 𝑐 𝑑 ,

Homework Homework 3.2