Answered: 0.6000x1 + 2000x2 = 20030.3076x1 −…

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

0.6000x1 + 2000x2 = 2003
0.3076x1 − 0.4010x2 = 1.137 Use four-digit decimal floating-point arithmetic,
and scale the system by multiplying
the first equation through by 1/2000 and the
second equation through by 1/0.4010. Solve the
scaled system using partial pivoting.

Expert Solution

Step 1 Given information:

The given system of linear equations:

$\begin{array}{rcl} 0.6000 x_{1} + 2000 x_{2} & = & 2003 \\ 0.3076 x_{1} - 0.4010 x_{2} & = & 1.137 \end{array}$

The objective is to multiply the first equation through by $\frac{1}{2000}$ and the second equation through by $\frac{1}{0.4010}$ and solve the scaled system using partial pivoting.

Step 2 Calculation:

Multiplying the first equation through by $\frac{1}{2000}$ and the second equation through by $\frac{1}{0.4010}$ .

$\begin{array}{rcl} \frac{0.6000}{2000} x_{1} + x_{2} & = & \frac{2003}{2000} \\ \frac{0.3076}{0.4010} x_{1} - x_{2} & = & \frac{1.137}{0.4010} \end{array}$

Simplify the above system.

$\begin{array}{rcl} 0.0003 x_{1} + x_{2} & = & 1.0015 \\ 0.767082294264 x_{1} - x_{2} & = & 2.83541147132 \end{array}$

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