Download presentation

Presentation is loading. Please wait.

Published byLaureen Edwards Modified over 7 years ago

1
14.3 Matrix Equations and Matrix Solutions to 2x2 Systems OBJ: Use the Inverse of a 2 x 2 Matrix to solve a system of equations

2
To find the inverse (A -1 ) of Matrix A EX: If A = 54 23 Find A -1 A 5 3 – 4 2 A -1 = 1 3-4 7 -2 5 Check your answer by finding A A -1 1 5 4 3-4 7 2 3 -2 5 If A = ab cd where A = ad – bc then A -1 = 1 d -b A -c a

3
Use matrices to solve the given system of equations: 5x + 4y = -2 2x + 3y = -5 This system of two equations in two unknowns can be replaced by a single matrix equation. A X = C 5 4 x -2 2 3 y = -5

4
Notice that the coefficient matrix: A = 5 4 2 3 is the matrix whose inverse was found in the previous example. A -1 = 1 3 -4 7 -2 5

5
If you left-multiply both sides of the matrix equation by A -1, you get: 1 3 -4 5 4 x 1 3 -4 -2 7 -2 5 2 3 y = 7 -2 5 -5 3 -2 + -4 -5 -2 -2 + 5 -5 1 7 0 x 1 14 7 0 7 y = 7 -21 1 0 x = 2 0 1 y -3 x = 2 y -3

6
Solve the matrix equation for X. 7 -2 3 -5 -1 5 -4 1 X – 0 4 = 2 -3 = + 7 -2 2 0 -4 1 X = 2 1 If you left-multiply both sides of the matrix equation by A -1 1 1 2 7 -2 1 1 2 2 0 -1 4 7 -4 1 X = -1 4 7 2 1 1 2 + 2 2 1 0 + 2 1 4 2 + 7 2 4 0 + 7 1 1 -1 0 1 6 2 -1 0 -1 X = -1 22 7 -6 -2 X = -22 -7

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