## CCSS.Math.Content.HSA.REI.C.9 - (+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 x 3 or greater).

Authors: National Governors Association Center for Best Practices, Council of Chief State School OfficersTitle: CCSS.Math.Content.HSA.REI.C.9 (+) Find The Inverse Of A Matrix If It... Reasoning with Equations & Inequalities - High School Algebra Mathematics Common Core State Standards

Publisher: National Governors Association Center for Best Practices, Council of Chief State School Officers, Washington D.C.

Copyright Date: 2010

(Page last edited 10/20/2014)

- Find the Determinant of a 3x3 Matrix - A 3x3 matrix is given and the student is asked to find the determinant. A form prompts the student to supply their answer. If the answer is correct, another problem can be provided. Five requests for hints are available for each problem where the general method for solving the determinant and then partial calculations specific to the given matrix, and then the answer are revealed.
- Find the Inverse of a Matrix If It Exists and Use It to Solve systems of Linear Equations - Students should already know how to form a matrix equation of AX = B from a system of linear equations and be familiar with the concept of inverse matrices. They will use the inverse of a matrix in order to solve for the variables of the matrix that is formed from given equations. Students should know that if the determinant of a square matrix is zero (ad – bc = 0), there is no inverse to the matrix. A quiz is provided.
- Finding the determinant of a 3x3 matrix - Finding the determinant of a 3x3 matrix (method 2) by alternating positive/negative/positive of the top row numbers times the determinant of the associated 2x2 submatrix.
- Finding the Determinant of a 3x3 Matrix - Method 1 - Finding the determinant of a 3x3 matrix (method 1) by adding top left to bottom right diagonals while subtracting top right to bottom left diagonals.
- Idea Behind Inverting a 2x2 Matrix - What the inverse of a matrix is. Examples of inverting a 2x2 matrix showing basic matrix multiplication, the concept of an identity matrix, the concepts of inverses and an inverse matrix, and the concept of the determinant. The inverted matrix is tested by multiplying it with the original matrix to result in the identity matrix.
- Inverse of a Matrix - Example of calculating the inverse of a 2x2 matrix, involving calculating the determinant and the adjucate of the matrix.
- Matrices To Solve a System of Equations - Using the inverse of a matrix to solve a system of equations. Example used is: 3x + 2y = 7 and -6x + 6y = 6.
- Matrices to Solve a Vector Combination Problem - Example based on using matrices to figure out if some combination of 2 vectors can create a 3rd vector. This is a stepping stone toward inverting matrices.
- Matrices: Inverse of a 2x2 Matrix - Student is asked to solve for the inverse of a 2x2 matrix or select "undefined" if an inverse does not exist. New problems are provided after each answer and score is kept over a timed interval. Explanation of wrong answers are provided.
- Singular Matrices - When and why you can't invert a matrix.