Explanation Given: The given system is as follows; x + y + z − 2 w = − 8 x − 2 y + 3 z + w = 18 2 x + 2 y + 2 z − 2 w = 10 2 x + y − z + w = 3 Calculation: Consider these two equations from the system; x + y + z − 2 w = − 8 2 x + 2 y + 2 z − 2 w = 10 Subtract the first equation from the second to get, 2 x + 2 y + 2 z − 2 w − ( x + y + z − 2 w ) = 10 − ( − 8 ) x + y + z = 18 Substitute x + y + z = 18 in the equation x + y + z − 2 w = − 8 to get the value of w , x + y + z − 2 w = − 8 18 − 2 w = − 8 − 2 w = − 8 − 18 − 2 w = − 26 So, w = 13 . Now, multiply the equation in the number 4th position by 2, so it becomes, x − 2 y + 3 z + w = 18 4 x + 2 y − 2 z + 2 w = 6 Add the above equations to get, x − 2 y + 3 z + w + 4 x + 2 y − 2 z + 2 w = 18 + 6 5 x + z + 3 w = 24 5 x + z = 24 − 3 ( 13 ) = 24 − 39 So, 5 x + z = − 15

MyLab Math with Pearson eText -- Combo Access Card (18-wk) for Algebra & Trigonometry

7th Edition

ISBN: 9780137393831

Author: ROBERT BLITZER

Publisher: Pearson Education (US)

See similar textbooks

Videos

Question

Chapter 8.2, Problem 52E

To determine

To calculate: The process to solve the x+y+z−2w=−8,x−2y+3z+w=18, 2x+2y+2z−2w=10 and 2x+y−z+w=3 system. Later to tell whether in the near future graphing utility is available to provide a geometric solution to the provided system.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.2, Problem 51E

Chapter 8.2, Problem 53E

Students have asked these similar questions

Assume {u1, U2, u3, u4} does not span R³. Select the best statement. A. {u1, U2, u3} spans R³ if u̸4 is a linear combination of other vectors in the set. B. We do not have sufficient information to determine whether {u₁, u2, u3} spans R³. C. {U1, U2, u3} spans R³ if u̸4 is a scalar multiple of another vector in the set. D. {u1, U2, u3} cannot span R³. E. {U1, U2, u3} spans R³ if u̸4 is the zero vector. F. none of the above

Select the best statement. A. If a set of vectors includes the zero vector 0, then the set of vectors can span R^ as long as the other vectors are distinct. n B. If a set of vectors includes the zero vector 0, then the set of vectors spans R precisely when the set with 0 excluded spans Rª. ○ C. If a set of vectors includes the zero vector 0, then the set of vectors can span Rn as long as it contains n vectors. ○ D. If a set of vectors includes the zero vector 0, then there is no reasonable way to determine if the set of vectors spans Rn. E. If a set of vectors includes the zero vector 0, then the set of vectors cannot span Rn. F. none of the above

Which of the following sets of vectors are linearly independent? (Check the boxes for linearly independent sets.) ☐ A. { 7 4 3 13 -9 8 -17 7 ☐ B. 0 -8 3 ☐ C. 0 ☐ D. -5 ☐ E. 3 ☐ F. 4 TH

Chapter 8 Solutions

MyLab Math with Pearson eText -- Combo Access Card (18-wk) for Algebra & Trigonometry

Knowledge Booster

$Algebra$

Learn more about

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

The process to solve the x + y + z − 2 w = − 8 , x − 2 y + 3 z + w = 18 , 2 x + 2 y + 2 z − 2 w = 10 and 2 x + y − z + w = 3 system. Later to tell whether in the near future graphing utility is available to provide a geometric solution to the provided system.

Solution Summary: The author explains the process to solve the x+y+z-2w=-8, 2x +2y + 2z+w = 18, and two-fold-y-z-w

Videos

To calculate: The process to solve the x+y+z−2w=−8,x−2y+3z+w=18, 2x+2y+2z−2w=10 and 2x+y−z+w=3 system. Later to tell whether in the near future graphing utility is available to provide a geometric solution to the provided system.

Want to see the full answer?

Chapter 8 Solutions