Warm-up

1. Warm-up 2 3 -1 A = 0 -5 4 B = -7 1 0 2 6 -6 2 C = 9 4 D = -3 2 -1 1. Find 8A 2. Find AC 3. Find CD 4. Find BD

2. 2x2 Matrices, Determinants, and Inverses Goal To evaluate determinants and inverses of 2x2 matrices and to use inverse matrices to solve equations Thinking Skill To make decisions after reflection and review

3. Definitions • Square Matrix • Matrix with the same number of rows as columns

4. Definitions • Multiplicative Identity Matrix • For an nxn matrix, the multiplicative identity matrix is an nxn square matrix I, or Inxn, with 1s along the main diagonal and 0s elsewhere.

5. Definitions • Multiplicative Inverse of a Matrix • If A and X are nxn matrices, and AX = XA = I, then X is the multiplicative inverse of A written as A-1 • Show that the matrices are multiplicative inverses -2 -5 -8 5 -3 -8 & 3 -2

6. Definitions • Determinant of a 2x2 matrix • The determinant of a 2x2 matrix is ad - bc • Notation det A • EX • Evaluate the determinant

7. Definitions • Inverse of a 2x2 matrix • Let A = . If det A 0, then A has an inverse. • If det A 0, then

8. Determine if it has an inverse…if so, find it [flip a and d, make b and c negative]

9. Using Inverse Matrices to solve equations • AX = B A-1(AX) = A-1B (A-1A)X = A -1B IX = A-1B X = A-1B

10. Steps Get in form AX = B Find A-1 Use X = A-1B Check Solving a Matrix Equation

11. Lesson Quiz • Is the inverse of ? How do you know? • Find the determinant of • Find the inverse of • Solve