Honor Trig/MA Inverses of 2 X 2 Matrices.

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Presentation transcript:

Honor Trig/MA Inverses of 2 X 2 Matrices

Inverse Transformations 2 Transformations, S and T, are inverse transformations if and only if S◦T = T◦S =

ad – bc If the determinant is = 0, then NO INVERSE EXISTS! recall: Determinant ad – bc If the determinant is = 0, then NO INVERSE EXISTS!

Example Show that the following 2 matrices are inverses: (SHOW THE INTERMEDIATE STEP!)

How do I find the inverse of a matrix? Step 1: Find the determinant! if it is equal to 0. Step 2: Perform the “switch”: Step 3: Multiply this matrix by 1/determinant

Find the inverse of Determinant: 1(4) - -3(5) = 19 “Switch” Multiply: Example Find the inverse of Determinant: 1(4) - -3(5) = 19 “Switch” Multiply:

A Couple of Notes about Inverses…. You may need to reduce the fractions after multiplying by 1/determinant! Do not leave as decimals: integers or fractions ONLY. You can check your answer in the calculator: Enter the matrix into calculator [A]-1 = inverse of a matrix MATH, FRAC, ENTER

Using Matrices to Solve A System Ax + By = C Dx + Ey = F Put into matrix form: Multiply by the inverse of coefficient matrix:

x=1 and y=1 Solve the system using matrices: 2x + 2y = 4 2x + y = 3 Example Solve the system using matrices: 2x + 2y = 4 2x + y = 3 x=1 and y=1

More Practice 1. Find the inverse of the following matrix: . 2. What would n have to be in the following matrix in order for the inverse to NOT exist? 3. Solve the system using matrices: 4x + 3y = 17 3x – 4y = 19

Closure Refer to the Cramer’s Rule Warm-Up. Verify your result by solving the system using the matrix method in this lesson.