Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Name Class 12-4 Date Reteaching Inverse Matrices and Systems ax by p a b x p as . • You can write the system cx dy q c d y q a b x • is the coefficient matrix, is the variable matrix, and c d y p q is the constant matrix. • Solve the matrix equation by multiplying both sides on the left by the inverse of the coefficient matrix, if it exists. 4 x 3 y 4 What is the solution of the system ? Solve using matrices. 3 x y 3 4 3 x 4 3 1 y 3 Write the system as a matrix equation. 3 1 Find the inverse of 4 3 1 3 1 1 3 1 13 13 the coefficient 3 1 det A 3 4 (1)(4) (3)(3) 3 4 3 4 matrix. 13 13 1 3 3 1 1 13 13 4 3 x 13 13 4 Isolate the 3 4 3 1 y 3 4 3 variable matrix by 13 13 13 13 multiplying both sides on the left by the inverse of the coefficient matrix. . 4 9 x 1 13 13 Simplify. y 12 12 0 13 13 The solution is (1, 0). Substitute the values in the original system to check your work. Exercises Solve each system of equations using a matrix equation. Check your answers. 2 x 7 y 3 x 5y 7 1. x 3y 5 x 4 y 6 2. x 3 y 1 5 x 16 y 5 3. Prentice Hall Algebra 2 • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 39 Name 12-4 Class Date Reteaching (continued) Inverse Matrices and Systems You can use a graphing calculator and matrices to solve a linear system. 4 x 5 y 6 z 50 What is the solution of the system x 2 y 3z 1 ? Solve using a graphing y z 3 Write the system as a matrix equation. Enter the coefficient matrix as matrix A. 4 5 6 x 50 1 2 3 y 1 0 1 1 z 3 Enter the constant matrix as matrix B. Multiply A1B to find the variable matrix. The solution is ( 11.6, 21.6, 18.6). Substitute the values in the original system to check your work. Exercises Solve each system of equations using a graphing calculator and matrices. Check your answers. 4x y z 0 4. 5 x 2 y 3z 15 6 x 5 y 5 z 52 0.5 x 1.5 y z 7 5. 3x 3 y 5 z 3 2 x y 2 z 1 x 2 y – z 19 –8 6. 2 x – 3 y y – 5 z 16 4 x 8 y 3z 7 y 5z 6 7. 2 x 5 y 1 Prentice Hall Algebra 2 • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 40