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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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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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

Logic and Functions

Probability and Statistics

Statistics

Theoretical and Mathematical Physics

Discrete 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.
$\{\begin{cases} 25 x + 61 y - 12 z = 25 \\ 18 x - 12 y + 7 z = 10 \\ 3 x + 4 y - z = - 4 \end{cases}$