/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 8 Write the augmented matrix for e... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 8

Write the augmented matrix for each system and give its dimension. Do not solve. $$\begin{aligned}&4 x-2 y+3 z-4=0\\\&3 x+5 y+z-7=0\\\&5 x-y+4 z-7=0\end{aligned}$$

Short Answer

Expert verified
The augmented matrix is \[\begin{bmatrix} 4 & -2 & 3 & | & 4 \ 3 & 5 & 1 & | & 7 \ 5 & -1 & 4 & | & 7 \end{bmatrix}\] and its dimension is \(3 \times 4\).

Step by step solution

01

Understand the System of Equations

The given system of equations is: \[\begin{aligned} &4x - 2y + 3z - 4 = 0 \ &3x + 5y + z - 7 = 0 \ &5x - y + 4z - 7 = 0 \end{aligned}\]. The goal is to write its augmented matrix and find the dimension of the matrix.
02

Isolate the Constants

Rewrite the system by isolating the constants on the right side: \[\begin{aligned} &4x - 2y + 3z = 4 \ &3x + 5y + z = 7 \ &5x - y + 4z = 7 \end{aligned}\].
03

Write the Coefficient Matrix

Extract the coefficients from each equation and arrange them into a matrix: \[\begin{bmatrix} 4 & -2 & 3 \ 3 & 5 & 1 \ 5 & -1 & 4 \end{bmatrix}\].
04

Write the Augmented Matrix

Combine the coefficient matrix with the constants to form the augmented matrix: \[\begin{bmatrix} 4 & -2 & 3 & | & 4 \ 3 & 5 & 1 & | & 7 \ 5 & -1 & 4 & | & 7 \end{bmatrix}\].
05

Find the Dimension of the Matrix

Determine the dimensions of the augmented matrix. The matrix has 3 rows and 4 columns, so its dimension is \(3 \times 4\).

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

System of Equations
A system of equations is a set of multiple equations that share the same set of unknowns. In this exercise, we are working with three equations and three unknowns: \(x\), \(y\), and \(z\).

One App. One Place for Learning.

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

Get started for free

Most popular questions from this chapter

Solve each problem. A glue company needs to make some glue that it can sell for \(120\) per barrel. It wants to use 150 barrels of glue worth \(100\) per barrel, along with some glue worth \(150\) per barrel and some glue worth \(190\) per barrel. It must use the same number of barrels of \(150\) and \(190\) glue. How much of the \(150\) and \(190\) glue will be needed? How many barrels of \(120\) glue will be produced?

Your friend missed the lecture on multiplying matrices. Explain to her the process of matrix multiplication.

Explain the process for finding the inverse of a matrix.

Solve each linear programming problem. Aid to Disaster Victims Earthquake victims in Haiti need medical supplies and bottled water. Each medical kit measures \(1 \mathrm{ft}^{3}\) and weighs 10 lb. Each container of water is also \(1 \mathrm{ft}^{3}\) but weighs \(20 \mathrm{lb}\). The plane can carry only \(80,000\) Ib with a total volume of \(6000 \mathrm{ft}^{3}\) Each medical kit will aid 4 people, and each container of water will serve 10 people. (a) How many of each should be sent to maximize the number of people helped? (b) If each medical kit could aid 6 people instead of 4, how would the results from part (a) change? PICTURE CANT COPY

Solve each problem. A sparkling-water distributor wants to make up 300 gal of sparkling water to sell for \(\$ 6.00\) per gallon. She wishes to mix three grades of water selling for \(\$ 9.00, \$ 3.00,\) and \(\$ 4.50\) per gallon, respectively. She must use twice as much of the S4.50 water as of the \(\$ 3.00\) water. How many gallons of each should she use?
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.