Q. 82 In Problems 75鈥� 82, algebraica... [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. 82 (page 757)

In Problems 75鈥� 82, algebraically solve each system of equations using any method you wish.
$\{\begin{cases} - 4 x + 3 y + 2 x = 6 \\ 3 x + y - z = - 2 \\ x + 9 y + z = 6 \end{cases}$

Short Answer

Expert verified

The given equation $\{\begin{cases} - 4 x + 3 y + 2 x = 6 \\ 3 x + y - z = - 2 \\ x + 9 y + z = 6 \end{cases}$ has determinant is zero,matrix Ais singular.Hence the system has no solution

Step by step solution

Step 1. Given information

The given information $\{\begin{cases} - 4 x + 3 y + 2 x = 6 \\ 3 x + y - z = - 2 \\ x + 9 y + z = 6 \end{cases}$

Step 2. Finding the values of x,y and z

Consider the equations $- 4 x + 3 y + 2 z = 6, 3 x + y - z = - 2 a n d x + 9 y + z = 6$ .To solve these equations we first convert them into matrix equation of the form $A X = B$

$[\begin{matrix} - 4 & 3 & 2 \\ 3 & 1 & - 1 \\ 1 & 9 & 1 \end{matrix}] [\begin{matrix} x \\ y \\ z \end{matrix}] = [\begin{matrix} 6 \\ - 2 \\ 6 \end{matrix}]$

Now solve this matrix equation we have to find the inverse matrix A.So,to check whether its inverse is possible or not,we find its determinant

$|\begin{matrix} - 4 & 3 & 2 \\ 3 & 1 & - 1 \\ 1 & 9 & 1 \end{matrix}| = - 4 \{1 (1) - 9 (- 1)\} - 3 \{3 (1) - 1 (- 1)\} + 2 \{3 (9) - 1 (1)\} = - 4 (1 + 9) - 3 (3 + 1) + 2 (27 - 1) = - 40 - 12 + 52 |\begin{matrix} - 4 & 3 & 2 \\ 3 & 1 & - 1 \\ 1 & 9 & 1 \end{matrix}| = 0$

As the determinant is zero,matrix Ais singular.Hence the system has no solution

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

In Problems 75鈥� 82, algebraically solve each system of equations using any method you wish.
$\{\begin{cases} - 4 x + 3 y + 2 x = 6 \\ 3 x + y - z = - 2 \\ x + 9 y + z = 6 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding the values of x,y and z

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Mechanics Maths

Pure Maths

Applied Mathematics

Logic and Functions

Probability and Statistics

Study anywhere. Anytime. Across all devices.

91影视

In Problems 75鈥� 82, algebraically solve each system of equations using any method you wish.-4x+3y+2x=63x+y-z=-2x+9y+z=6

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding the values of x,y and z

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Mechanics Maths

Pure Maths

Applied Mathematics

Logic and Functions

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In Problems 75鈥� 82, algebraically solve each system of equations using any method you wish.
$\{\begin{cases} - 4 x + 3 y + 2 x = 6 \\ 3 x + y - z = - 2 \\ x + 9 y + z = 6 \end{cases}$