A system of linear equations is given.2x -3x + 2y - 3z =x - 4y + 5z = -1y + z =1(a) Find the complete solution of the system, or show that there is no solution. (If there is no solution, enter NO SOLUTION. If the system is dependent, enter your answer in terms of t.)(х, у, 2) %3D(b) State whether the system is inconsistent, dependent, or neither.O inconsistentO dependentO neither

Answered: A system of linear equations is given.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

A system of linear equations is given.
2x -
3x + 2y - 3z =
x - 4y + 5z = -1
y + z =
1
(a) Find the complete solution of the system, or show that there is no solution. (If there is no solution, enter NO SOLUTION. If the system is dependent, enter your answer in terms of t.)
(х, у, 2) %3D
(b) State whether the system is inconsistent, dependent, or neither.
O inconsistent
O dependent
O neither

Expert Solution

Step 1

Given linear equation is

$2 x - y + z = 0 3 x + 2 y - 3 z = 1 x - 4 y + 5 z = - 1$

Step 2

Now (a)

$2 x - y + z = 0 . . . . (1) 3 x + 2 y - 3 z = 1 . . . . (2) x - 4 y + 5 z = - 1 . . . . (3) s o l v e e q u a t i o n (1), (2) a n d (3) 2 x - y + z = 0 x = \frac{y - z}{2} p u t t h e v a l u e x = \frac{y - z}{2} i n (2) e q u a t i o n 3 (\frac{y - z}{2}) + 2 y - 3 z = 1 3 y - 3 z + 4 y - 6 z = 2 7 y - 9 z = 2 y = \frac{2 + 9 z}{7} N o w x = \frac{\frac{2 + 9 z}{7} - z}{2} x = \frac{2 + 9 z - 7 z}{14} x = \frac{2 + 2 z}{14} x = \frac{1 + z}{7} S o x = \frac{1 + z}{7}, y = \frac{2 + 9 z}{7} P u t t h e v a l u e o f x a n d y i n a n y a b o v e e q u a t i o n (1), (2) a n d (3) \frac{1 + z}{7} - 4 (\frac{2 + 9 z}{7}) + 5 z = - 1 1 + z - 8 - 36 z + 35 z = - 7 0 = 0 T h u s t h e r e i s i n f i n i t l y m a n y s o l u t i o n .$

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