Warm-up 23-1 A = 0-54 B = C = 9 4 D = Find 8A 2. Find AC 3. Find CD 4. Find BD

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

Definitions Square Matrix Matrix with the same number of rows as columns

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

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 &3-2

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

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

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

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

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

Lesson Quiz 1. Is the inverse of ? How do you know? 2. Find the determinant of 3. Find the inverse of 4. Solve