Explanation Given: The system of equations is, 5 x − 4 y + 2 z = 6 5 x + 3 y − z = 11 15 x − 5 y + 3 z = 23 Approach: Gauss-Jordan Method of Solving a Linear System Write each equation so that variable terms are in the same order on the left side of the equal sign and constants are on the right. Write the augmented matrix that corresponds to the system. Use row operations to transform the first column so that all elements except the element in the first row are zero. Use row operations to transform the second column so that all elements except the element in the second row are zero. Use row operations to transform the third column so that all elements except the element in the third row are zero. Continue in this way. when possible, until the last row is written in the form [ 0 0 0 . . . 0 j k ] Where j and k are constants with j ≠ 0 . When this is not possible, continue until every row has more zeros on the left than the previous row (except possibly for any rows of all zeros at the bottom of the matrix), and the first nonzero entry in each row is the only nonzero entry in its column. Multiply each row by the reciprocal of the nonzero element in that row. Calculation: Consider the system of equations. 5 x − 4 y + 2 z = 6 5 x + 3 y − z = 11 15 x − 5 y + 3 z = 23 Write the augmented matrix for the system of equations. [ 5 − 4 2 6 5 3 − 1 11 15 − 5 3 23 ] Use row operations and achieve the format on the left side of the vertical line as, [ 1 0 0 0 1 0 0 0 1 ] The first step is to reduce the first column of row 2 to zero. Apply the row operation R 2 − R 1 → R 2 . [ 5 − 4 2 6 5 3 − 1 11 15 − 5 3 23 ] → R 2 − R 1 → R 2 [ 5 − 4 2 6 0 7 − 3 5 15 − 5 3 23 ] The second step is to reduce the first column of row 3 to zero. Apply the row operation R 3 − 3 R 1 → R 3 . [ 5 − 4 2 6 0 7 − 3 5 15 − 5 3 23 ] → R 3 − 3 R 1 → R 3 [ 5 − 4 2 6 0 7 − 3 5 0 7 − 3 5 ] The third step is to reduce the second column of row 1 to zero. Apply the row operation 4 R 2 + 7 R 1 → R 1 . [ 5 − 4 2 6 0 7 − 3 5 0 7 − 3 5 ] → 4 R 2 + 7 R 1 → R 1 [ 35 0 2 62 0 7 − 3 5 0 7 − 3 5 ] The fourth step is to reduce the second column of row 3 to zero

2nd Edition

ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

See similar textbooks

Videos

Question

Chapter 10.1, Problem 33E

To determine

The solution to the system of equations 5x−4y+2z=65x+3y−z=1115x−5y+3z=23 using Gauss-Jordan method.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 10.1, Problem 32E

Chapter 10.1, Problem 34E

Students have asked these similar questions

Let w(x, y, z) = x² + y² + z² where x = sin(-3), y = cos(−8t), z = e5t. Calculate dw dt dx dy dz by first finding & and using the chain rule. dt' dt dt

z = x²+xy³, x = uv²+w³, y=u+vew Əz then find: when u = −3, v = 2, w = 0 მო

Let z(x, y) = -3x² + 8y² where x = 4s + 2t & y = −5s - 8t. Calculate მ მ მე მყ მეთ მყ & by first finding and using the chain rule. მე Ət მs’მვ’მt It

Chapter 10 Solutions

Calculus For The Life Sciences

Ch. 10.1 - YOUR TURN Use the Gauss-Jordan method to solve the...Ch. 10.1 - Prob. 2YT Ch. 10.1 - Prob. 3YT Ch. 10.1 - Write the augmented matrix for each system. Do not...Ch. 10.1 - Write the augmented matrix for each system. Do not...Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Write the system of equations associated with each...Ch. 10.1 - Write the system of equations associated with each...Ch. 10.1 - Prob. 7E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The solution to the system of equations 5 x − 4 y + 2 z = 6 5 x + 3 y − z = 11 15 x − 5 y + 3 z = 23 using Gauss-Jordan method.

Solution Summary: The author explains the Gauss-Jordan method of Solving a Linear System.

Videos

The solution to the system of equations 5x−4y+2z=65x+3y−z=1115x−5y+3z=23 using Gauss-Jordan method.

Want to see the full answer?

Chapter 10 Solutions