Q. 74 Use the idea behind Example 聽wi... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 11: Q. 74 (page 756)

Use the idea behind Example with a graphing utility to solve the following systems of equations. Round answers to two decimal places.
$\{\begin{cases} 25 x + 61 y - 12 z = 25 \\ 18 x - 12 y + 7 z = 10 \\ 3 x + 4 y - z = - 4 \end{cases}$

Short Answer

Expert verified

Thus the values of variables are $x = 0.54, y = 0.01 & z = 0.052$

Step by step solution

Step 1.Given information

Given equations $\begin{array}{l} 25 x + 61 y - 12 z = 25 \\ 18 x - 12 y + 7 z = 10 \\ 3 x + 4 y - z = - 4 \end{array}$

Step 2.Convert the equation

Convert these equation into matrix equation of the form $A X = B$

$[\begin{matrix} 25 & 61 & - 12 \\ 18 & - 2 & 4 \\ 8 & 35 & 21 \end{matrix}] [\begin{matrix} x \\ y \\ z \end{matrix}] = [\begin{matrix} 25 \\ 10 \\ - 4 \end{matrix}]$

Step 3.Inverse matrix

To find the solution we find the inverse of the matrix $[\begin{matrix} 25 & 61 & - 12 \\ 18 & - 2 & 4 \\ 8 & 35 & 21 \end{matrix}]$

The inverse matrix = $[\begin{matrix} 0.00 & 0.05 & - 0.01 \\ 0.01 & - 0.02 & 0.01 \\ - 0.02 & 0.01 & 0.03 \end{matrix}]$

Step 4.Substitution

$[\begin{matrix} x \\ y \\ z \end{matrix}] = [\begin{matrix} 0.00 & 0.05 & - 0.01 \\ 0.01 & - 0.02 & 0.01 \\ - 0.02 & 0.01 & 0.03 \end{matrix}] [\begin{matrix} 25 \\ 10 \\ 4 \end{matrix}]$

$[\begin{matrix} x \\ y \\ z \end{matrix}] = [\begin{matrix} 0.54 \\ 0.01 \\ - 0.52 \end{matrix}]$

Step 5. The solution

Thus the values of variables are $x = 0.54, y = 0.01 & z = 0.052$

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91影视

Use the idea behind Example with a graphing utility to solve the following systems of equations. Round answers to two decimal places.
$\{\begin{cases} 25 x + 61 y - 12 z = 25 \\ 18 x - 12 y + 7 z = 10 \\ 3 x + 4 y - z = - 4 \end{cases}$

Short Answer

Step by step solution

Step 1.Given information

Step 2.Convert the equation

Step 3.Inverse matrix

Step 4.Substitution

Step 5. The solution

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Most popular questions from this chapter

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91影视

Use the idea behind Example with a graphing utility to solve the following systems of equations. Round answers to two decimal places.25x+61y-12z=2518x-12y+7z=103x+4y-z=-4

Short Answer

Step by step solution

Step 1.Given information

Step 2.Convert the equation

Step 3.Inverse matrix

Step 4.Substitution

Step 5. The solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Theoretical and Mathematical Physics

Logic and Functions

Statistics

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Use the idea behind Example with a graphing utility to solve the following systems of equations. Round answers to two decimal places.
$\{\begin{cases} 25 x + 61 y - 12 z = 25 \\ 18 x - 12 y + 7 z = 10 \\ 3 x + 4 y - z = - 4 \end{cases}$