4.7 Identity and Inverse Matrices and Solving Systems of Equations Objectives: 1.Determine whether two matrices are inverses. 2.Find the inverse of a 2x2.

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Presentation transcript:

4.7 Identity and Inverse Matrices and Solving Systems of Equations Objectives: 1.Determine whether two matrices are inverses. 2.Find the inverse of a 2x2 matrix 3.Write matrix equations for systems of equations 4.Solve systems of equations using matrix equations

Identity Matrix An identity matrix is a matrix that when multiplied by another matrix gives the same matrix back. (like multiplying a number by 1) The Diagonal from left to right contains only the number 1 and all other elements are 0.

Example of How the Identity Matrix works Multiply (you should get the same matrix back)

Inverses Two matrices are inverses if their products are the identity matrix. To determine if they are inverses, multiply the matrices to see if the product yields the identity matrix. Example: They are inverses.

Finding Inverses The inverse of 2x2 matrix is where ad-bc≠0

Example Find the inverse.

Using Matrices to solve Systems of Equations To solve a system using a matrix, use the inverse. For the system 5x+3y=13 4x+7y=-8 Create 3 matrices:

Continued Find inverse of coefficient matrix. Multiply this by the other side (what x and y are set = to). This is like dividing by what is being multiplied by the variable. Inv= multiply this by the other side so (5,-4)

Try One Solve using an inverse matrix. 3x+y=13 4x-2y=24

Homework p. 199, 10, 20, 26 p. 206, 20, 24, 28, 30