Warmup A B 2 0 3 5 1

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

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

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

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

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

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

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

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 l AX = B A-1(AX) = A-1 B (A-1 A)X = A -1 B IX = A-1 B

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

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