Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

Solve the linear system of equations. You may use technology.
$| \begin{matrix} 3 X + 6 y + 14 z = 22 \\ 7 X + 14 y + 30 z = 46 \\ 4 X + 8 y + 7 z = 6 \end{matrix} |$

For the given system of equation there is unique solution. $Y = - 6, y = 2, z = 2$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Augmented matrix

Solving system of equations using gauss Jordan’s elimination method.

First of all we will make the augmented matrix to the corresponding system of equations.

$|\begin{matrix} 3 X + 6 y + 14 Z = 22 \\ 7 X + 14 y + 30 z = 46 \\ 4 X + 8 y + 7 Z = 6 \end{matrix}|$

Corresponding augmented matrix

$[\begin{matrix} 3 & 6 & 14 \\ 7 & 14 & 30 \\ 4 & 8 & 7 \end{matrix} \begin{matrix} 22 \\ 46 \\ 6 \end{matrix}]$

Step 2: Solving the Augmented matrix

$[\begin{matrix} 3 & 6 & 14 \\ 7 & 14 & 30 \\ 4 & 8 & 7 \end{matrix} \begin{matrix} 22 \\ 46 \\ 6 \end{matrix}] R_{1} \leftrightarrow R_{3} R_{1} \to R_{1} - R_{3} [\begin{matrix} 1 & 2 & - 7 \\ 7 & 14 & 30 \\ 3 & 6 & 14 \end{matrix} \begin{matrix} - 16 \\ 46 \\ 22 \end{matrix}]$

$R_{2} \to R_{2} - 7 R_{1} R_{3} \to R_{3} - 3 R_{1} [\begin{matrix} 1 & 2 & - 7 \\ 0 & 0 & 79 \\ 0 & 0 & 35 \end{matrix} \begin{matrix} - 16 \\ 2 \\ 2 \end{matrix}] R_{2} \to \frac{1}{79} R_{2} R_{3} \to \frac{1}{35} - R_{3} [\begin{matrix} 1 & 2 & - 7 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \end{matrix} \begin{matrix} - 16 \\ 2 \\ 2 \end{matrix}]$

Step 3:Value of variables

Corresponding system of equations will be

$|\begin{matrix} X = - 2 y + 7 Z - 16 \\ y = 2 \\ Z = 2 \end{matrix}|$

Hence, the solution of equation will be $x = - 6, y = 2 z = 2$ .

Step 4: Final answer

For the given system of equation there is unique solution $x = - 6, y = 2 z = 2$ .

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Linear Algebra With Applications

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Short Answer

Solve the linear system of equations. You may use technology.
$| \begin{matrix} 3 X + 6 y + 14 z = 22 \\ 7 X + 14 y + 30 z = 46 \\ 4 X + 8 y + 7 z = 6 \end{matrix} |$

Step by Step Solution

Step 1: Augmented matrix

Step 2: Solving the Augmented matrix

Step 3:Value of variables

Step 4: Final answer

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Linear Algebra With Applications

Answers without the blur.

Short Answer

Solve the linear system of equations. You may use technology.|3X+6y+14z=227X+14y+30z=464X+8y+7z=6|

Step by Step Solution

Step 1: Augmented matrix

Step 2: Solving the Augmented matrix

Step 3:Value of variables

Step 4: Final answer

Most popular questions for Math Textbooks

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Recommended explanations on Math Textbooks

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Pure Maths

Solve the linear system of equations. You may use technology.
$| \begin{matrix} 3 X + 6 y + 14 z = 22 \\ 7 X + 14 y + 30 z = 46 \\ 4 X + 8 y + 7 z = 6 \end{matrix} |$