Bellwork 1) Multiply. 3) Find the determinant. 2) Multiply.

Answers

3.8A Use Inverse Matrices to solve linear systems Algebra II

Identity In other words, 5 * __= 5? What does “identity” mean to you? What is the multiplicative identity for the real numbers? In other words, 5 * __= 5? The identity for multiplication is 1 because anything multiplied by 1 will be itself.

a * a-1= 1 In other words, 5 * ___=1? What do we multiply by to get the identity? In other words, 5 * ___=1? a * a-1= 1 Any number multiplied by its inverse will be the identity.

A * A-1= I A-1 *A = I Identity Matrix Any matrix multiplied by its inverse will be the identity matrix. A * A-1= I A-1 *A = I 2x2 Identity Matrix

Identity Matrix Just like 5*1 = 5… AI= A IA= A Or

Determine whether A and B are inverses. Find out if AB = I If so, then yes they’re inverses. If not, then no they’re not inverses. Use your calculator. YES

The Inverse of a 2x2 Matrix As long as ad-cb =0 If ad-cb=0, then the matrix has no inverse!!!!

Ex. 1 Find A-1, if it exists. A-1=

Ex. 2 Find A-1, if it exists. Does not exist, because it’s not square.

Solving Matrix Equations Suppose ax = b How do you solve for x? We cannot divide matrices, but we can multiply by the inverse. A-1 AX = B A-1 IX = A-1B X = A-1B

Ex. 3 Solving a Matrix Equation Solve the matrix equation AX=B for the 2x2 matrix X

Step 2: Multiply both sides of the equation Step 1: find A-1 A-1= Step 2: Multiply both sides of the equation By A-1 on the left

You can check the Solution by mult AX to see if you get B

Assignment

Inverses What does “inverse” mean to you? What is the inverse of multiplication?

Determine whether A and B are inverses. NO