1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lubov Fominskaja [6]
3 years ago
13

What would you have to know about the pivot columns in an augmented matrix in order to know that the linear system is consistent

and has a unique solution?
Computers and Technology
1 answer:
Scrat [10]3 years ago
8 0

Answer:

The Rouché-Capelli Theorem. This theorem establishes a connection between how a linear system behaves and the ranks of its coefficient matrix (A) and its counterpart the augmented matrix.

rank(A)=rank\left ( \left [ A|B \right ] \right )\:and\:n=rank(A)

Then satisfying this theorem the system is consistent and has one single solution.

Explanation:

1) To answer that, you should have to know The Rouché-Capelli Theorem. This theorem establishes a connection between how a linear system behaves and the ranks of its coefficient matrix (A) and its counterpart the augmented matrix.

rank(A)=rank\left ( \left [ A|B \right ] \right )\:and\:n=rank(A)

rank(A)

Then the system is consistent and has a unique solution.

<em>E.g.</em>

\left\{\begin{matrix}x-3y-2z=6 \\ 2x-4y-3z=8 \\ -3x+6y+8z=-5  \end{matrix}\right.

2) Writing it as Linear system

A=\begin{pmatrix}1 & -3 &-2 \\  2& -4 &-3 \\ -3 &6  &8 \end{pmatrix} B=\begin{pmatrix}6\\ 8\\ 5\end{pmatrix}

rank(A) =\left(\begin{matrix}7 & 0 & 0 \\0 & 7 & 0 \\0 & 0 & 7\end{matrix}\right)=3

3) The Rank (A) is 3 found through Gauss elimination

(A|B)=\begin{pmatrix}1 & -3 &-2  &6 \\  2& -4 &-3  &8 \\  -3&6  &8  &-5 \end{pmatrix}

rank(A|B)=\left(\begin{matrix}1 & -3 & -2 \\0 & 2 & 1 \\0 & 0 & \frac{7}{2}\end{matrix}\right)=3

4) The rank of (A|B) is also equal to 3, found through Gauss elimination:

So this linear system is consistent and has a unique solution.

You might be interested in
As a student, why do you need to know and follow the steps printing a <br><br>document?​
Kazeer [188]
So I am able to print my math notes and keep up in geometry.
7 0
3 years ago
Read 2 more answers
When you evaluate the use of digital media, how has it affected the newspaper business? The rise of digital media has caused new
Harrizon [31]

Answer:

The rise of digital media has caused newspaper subscriptions to decline significantly because people are finding their news online.

It is A

3 0
3 years ago
Write a program to insert student grade and print the following
tangare [24]

Answer:

The answer is the program, in the explanation

Explanation:

I am going to write a C program.

int main(){

int grade = -1; /*The grade will be read to this variable*/

/*This loop will keep repeating until a valid grade is inserted*/

while(grade < 0 || grade > 100){

         printf("Insert the student's grade: %n");

         scanf("%d", &grade);

}

/*The conditional according to the grade value*/

if (grade >= 90){

     printf("Your grade is A\n");

}

else if (grade >= 80 && grade < 90){

     printf("Your grade is B\n");

}

else if (grade >= 70 && grade < 80){

     printf("Your grade is C\n");

}

else if (grade >= 60 && grade < 70){

     printf("Your grade is D\n");

}

else{

    printf("You got a failling grade\n");

}

return 0;

}

8 0
4 years ago
This is a program that calculates information about orders of shirts and pants. All orders have a quantity and a color. Write a
LuckyWell [14K]

Answer:

Check the explanation

Explanation:

// Clothing.java

public class Clothing {

//Declaring instance variables

private int quantity;

private String color;

//Zero argumented constructor

public Clothing() {

this.quantity = 0;

this.color = "";

}

//Parameterized constructor

public Clothing(int quantity, String color) {

this.quantity = quantity;

this.color = color;

}

// getters and setters

public int getQuantity() {

return quantity;

}

public void setQuantity(int quantity) {

this.quantity = quantity;

}

public String getColor() {

return color;

}

public void setColor(String color) {

this.color = color;

}

public double calculatePrice()

{

return 0.0;

}

}

_____________________________

// Pants.java

public class Pants extends Clothing {

//Declaring instance variables

private int waist;

private int inseam;

//Zero argumented constructor

public Pants() {

this.waist = 0;

this.inseam = 0;

}

//Parameterized constructor

public Pants(int quantity, String color, int waist, int inseam) {

super(quantity, color);

setWaist(waist);

setInseam(inseam);

}

// getters and setters

public int getWaist() {

return waist;

}

public void setWaist(int waist) {

if (waist > 0)

this.waist = waist;

}

public int getInseam() {

return inseam;

}

public void setInseam(int inseam) {

if (inseam > 0)

this.inseam = inseam;

}

public double calculatePrice() {

double tot = 0;

if (waist > 48 || inseam > 36) {

tot = 65.50;

} else {

tot = 50.0;

}

return tot;

}

}

__________________________

// Shirt.java

public class Shirt extends Clothing {

//Declaring instance variables

private String size;

//Zero argumented constructor

public Shirt() {

this.size = "";

}

//Parameterized constructor

public Shirt(int quantity, String color, String size) {

super(quantity, color);

this.size = size;

}

// getters and setters

public String getSize() {

return size;

}

public void setSize(String size) {

this.size = size;

}

public double calculatePrice() {

double tot = 0;

if (size.equalsIgnoreCase("S")) {

tot = getQuantity() * 11.00;

} else if (size.equalsIgnoreCase("M")) {

tot = getQuantity() * 12.50;

} else if (size.equalsIgnoreCase("L")) {

tot = getQuantity() * 15.00;

} else if (size.equalsIgnoreCase("XL")) {

tot = getQuantity() * 16.50;

} else if (size.equalsIgnoreCase("XXL")) {

tot = getQuantity() * 18.50;

}

return tot;

}

}

___________________________

//Test.java

import java.util.ArrayList;

public class Test {

public static void main(String[] args) {

int totShirts=0,totPants=0;

double sprice=0,pprice=0,totWaist=0,totinseam=0,avgWaist=0,avginseam=0;

int cnt=0;

ArrayList<Clothing> clothes=new ArrayList<Clothing>();

Shirt s=new Shirt(8,"Green","XXL");

Pants p1=new Pants(6,"Brown",48,30);

Pants p2=new Pants(4,"Blue",36,34);

clothes.add(s);

clothes.add(p1);

clothes.add(p2);

for(int i=0;i<clothes.size();i++)

{

if(clothes.get(i) instanceof Shirt)

{

Shirt s1=(Shirt)clothes.get(i);

totShirts+=s1.getQuantity();

sprice+=s1.calculatePrice();

}

else if(clothes.get(i) instanceof Pants)

{

Pants pa=(Pants)clothes.get(i);

totPants+=pa.getQuantity();

pprice+=pa.calculatePrice();

totinseam+=pa.getInseam();

totWaist+=pa.getWaist();

cnt++;

}

}

System.out.println("Total number of shirts :"+totShirts);

System.out.println("Total price of Shirts :"+sprice);

System.out.println("Total number of Pants :"+totPants);

System.out.println("Total price of Pants :"+pprice);

System.out.printf("Average waist size is :%.1f\n",totWaist/cnt);

System.out.printf("Average inseam length is :%.1f\n",totinseam/cnt);

 

}

}

_________________________

Output:

Total number of shirts :8

Total price of Shirts :148.0

Total number of Pants :10

Total price of Pants :100.0

Average waist size is :42.0

Average inseam length is :32.0

4 0
4 years ago
Select the correct answer.
snow_tiger [21]

Answer: I think it's D.

Explanation: I'm sorry if I chose the wrong answer, I'm not too good with stuff like this.

3 0
2 years ago
Other questions:
  • Caroline has been asked to find a standard to guide her company’s choices in implementing information security management system
    13·1 answer
  • I only want someones opinion on this not anything you would find in a book.
    7·1 answer
  • Assume a TCP segment consisting of 1500 bits of data and 160 bits of header is sent to the IP layer, which appends 120 bits of h
    14·1 answer
  • When applying a filter to a text layer, how can you ensure that the types editability is not lost
    12·1 answer
  • which of these variable declarations will the variable remain uninitialized unless it is explicitly initialized?1)Declaration of
    5·1 answer
  • True or false. The CPU requires it's own power from the power supply, and can't receive power from the motherboard.
    9·1 answer
  • Write a query that returns the first name of a student whose last name is "Patil" and is in the Ravenclaw house.
    9·1 answer
  • You can filter the data based on certain specific conditions in Excel 2013 true or false​
    8·1 answer
  • Give four example of computer virus​
    13·1 answer
  • _______ are useful when you want the user to select one choice from several possible choices. Radio buttons Check boxes Buttons
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!