1. Problem 1: Solve the linear system3x + 2yz = 5x+y+z=6-x+2y + 2z = 6by hand. Us a stopwatch to time your self and see how long it takes.Check your answer. If you got it right stop the timer. If not, try again.Once you are sure you have a correct answer, note the time.Now repeat using the Gaussian elimination algorithm we wrote in class,and the built in version in the numpy library. How much faster arethey than working by hand?

3x+2y-z=5 ix+y+z=6 ii -x+2y+2z=6 iiii+iiii3y+3z=12⇒y+z=4…

Answered: Problem 1: Solve the linear system 3x +…

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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1. Problem 1: Solve the linear system
3x + 2yz = 5
x+y+z=6
-x+2y + 2z = 6
by hand. Us a stopwatch to time your self and see how long it takes.
Check your answer. If you got it right stop the timer. If not, try again.
Once you are sure you have a correct answer, note the time.
Now repeat using the Gaussian elimination algorithm we wrote in class,
and the built in version in the numpy library. How much faster are
they than working by hand?

Expert Solution

Step 1: Solving the system of equation by method of elimination

$3 x + 2 y - z = 5 (i) x + y + z = 6 (i i) - x + 2 y + 2 z = 6 (i i) (i i) + (i i i i) 3 y + 3 z = 12 \Rightarrow y + z = 4 (a) ∴ x + y + z = 6 \Rightarrow x + 4 = 6 \Rightarrow x = 2 3 x + 2 y - z = 5 \Rightarrow 6 + 2 y - z = 5 \Rightarrow 2 y - z = - 1 \Rightarrow 2 y - (4 - y) = - 1 (f r o m (a)) \Rightarrow 3 y = 3 \Rightarrow y = 1 ∴ z = 3$