Using Matrices to Solve Systems of Equations Honors

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

Essential Stuff: • Essential Questions: • How do you use matrices to solve systems of equations? • How do you find the determinants of 2 x 2 and 3 x 3 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.

Matrices: • Allow us to organize and manipulate data. • Can also be used to solve systems. – Augmented Matrices

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

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

Determinants • 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… det. A = ad – bc A=

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 •

To find the inverse of a 2 x 2 matrix use the following formula:

Homework 3. 2