Explanation Given: The system of equations are 5 x + 2 z = 3 2 x + 2 y + z = 4 − 3 x + y − z = 5 Formula used A system of equations with the same number of equations as variables is written in matrix form as AX = B, where A is the square matrix of coefficients, X is the column matrix of variables, and B is the column matrix of constants. If A has an inverse, then the unique solution of the system is X = A -1 B. Calculation: Consider the provided system of equations: 5 x + 2 z = 3 2 x + 2 y + z = 4 − 3 x + y − z = 5 Now create a 3 × 3 matrix with the coefficients of the variable provided in the system of equation. Therefore, A = [ 5 0 2 2 2 1 − 3 1 − 1 ] Similarly, form a matrix 3 × 1 of the constants written on the right-hand side of the provided system of equations Therefore, B = [ 3 4 5 ] Now rewrite the equation as, A X = B Where X = [ x y z ] X = A − 1 B Now to solve this matrix equation, calculate the inverse of the matrix A . Therefore, A A − 1 = Ι [ 1 2 3 1 4 2 0 1 − 1 ] A − 1 = [ 1 0 0 0 1 0 0 0 1 ] Use the transformation R 2 → R 2 − R 1 [ 1 2 3 1 − 1 4 − 2 2 − 3 0 1 − 1 ] A − 1 = [ 1 0 0 0 − 1 1 − 0 0 − 0 0 0 1 ] [ 1 2 3 0 2 − 1 0 1 − 1 ] A − 1 = [ 1 0 0 − 1 1 0 0 0 1 ] Use the transformation R 3 → 2 R 3 − R 2 [ 1 2 3 0 2 − 1 0 − 0 2 − 2 − 2 + 1 ] A − 1 = [ 1 0 0 − 1 1 0 0 + 1 0 − 1 2 − 0 ] [ 1 2 3 0 2 − 1 0 0 − 1 ] A − 1 = [ 1 0 0 − 1 1 0 1 − 1 2 ] Use the transformation R 2 → R 2 − R 3 [ 1 2 3 0 − 0 2 − 0 − 1 + 1 0 0 − 1 ] A − 1 = [ 1 0 0 − 1 − 1 1 + 1 0 − 2 1 − 1 2 ] [ 1 2 3 0 2 0 0 0 − 1 ] A − 1 = [ 1 0 0 − 2 2 − 2 1 − 1 2 ] Use the transformation R 1 → R 1 − R 2 [ 1 − 0 2 − 2 3 − 0 0 2 0 0 0

MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE

11th Edition

ISBN: 9781323751671

Author: Lial

Publisher: PEARSON C

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Chapter 6.6, Problem 11E

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To calculate: Use the inverse of the coefficient matrix to solve each system of equation.

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MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE

Ch. 6.1 - Checkpoint1 Use the substitution method tosolve...Ch. 6.1 - Checkpoint 2 Use the elimination method to solve...Ch. 6.1 - Checkpoint 3 Solve the system of equations . Draw...Ch. 6.1 - Checkpoint 4 Solve the following system: Ch. 6.1 - Checkpoint 5 Solve the system Draw the graph of...Ch. 6.1 - Prob. 6CP Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Use substitution to solve each system. (See...Ch. 6.1 - Use substitution to solve each system. (See...

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