Chapter 11: Q. 82 (page 757)

In Problems 75– 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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In Problems 75– 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

Geometry

Statistics

Discrete Mathematics

Applied Mathematics

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In Problems 75– 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

Geometry

Statistics

Discrete Mathematics

Applied Mathematics

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

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