Download presentation

Presentation is loading. Please wait.

Published byLynette Christal Shepherd Modified over 8 years ago

1
12.4 Inverses of Matrices

2
Remember if A and B are inverses, AB = I and BA = I *only square matrices can have multiplicative inverses* Ex 1) Show that matrix B is the multiplicative inverse of matrix A.

3
To find the inverse of a square 2 × 2 matrix, we: (1)Find the determinant ad – bc (2)Make some changes in your matrix: (3)Multiply Ex 2) Find the multiplicative inverse. det = 27 – 28 = –1 switch change sign

4
For 3 × 3 and higher, we can use a calculator! Ex 3) Find the multiplicative inverse. 2 nd MATRIX EDIT [A] 3 × 3 enter data QUIT 2 nd MATRIX choose [A] [A] –1 = yikes! change to fractions MATH 1: ►Frac *arrow over to see the rest*

5
We can use inverses to solve for an unknown matrix *Be careful of the order* If A, X, and B are matrices, and AX = B to “get rid” of A, we multiply by A –1 A –1 (AX) = A –1 B X = A –1 B (must be in this order!) Ex 4) Solve for X.

6
Ex 5) Solve for X.(Use your calculator!) ↑ enter for matrix A ↑ enter for matrix B X = A –1 B

7
We can take a system of equations and turn it into a matrix equation to then solve! Ex 6) Set up the matrices to solve the system (We’re not going to solve this one – just set it up. But you solve in the homework!) coefficients ↑ represents answers You continue to solve like the previous examples

8
Homework #1204 Pg 624 #1–13 odd, 16, 21, 23, 31, 39, 41

Similar presentations

© 2023 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google