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
Alexxx [7]
3 years ago
10

Suppose has a solution. Explain why the solution is unique precisely when has only the trivial solution. Choose the correct answ

er.
A. Since is​ inconsistent, then the solution set of is also inconsistent. The solution set of is inconsistent if and only if has only the trivial solution.
B. Since is​ consistent, then the solution is unique if and only if there is at least one free variable in the corresponding system of equations. This happens if and only if the equation has only the trivial solution.
C. Since is​ consistent, its solution set is obtained by translating the solution set of . So the solution set of is a single vector if and only if the solution set of is a single​ vector, and that happens if and only if has only the trivial solution.
D. Since is​ inconsistent, its solution set is obtained by translating the solution set of . For to be​ inconsistent, has only the trivial solution
Mathematics
1 answer:
Margarita [4]3 years ago
5 0

Complete question is;

Suppose Ax = b has a solution. Explain why the solution is unique precisely when Ax = 0 has only the trivial solution. Choose the correct answer.

A. Since Ax = b is inconsistent, its solution set is obtained by translating the solution set of Ax = 0. For Ax = b to be inconsistent, Ax = 0 has only the trivial solution.

B. Since Ax = b is consistent, its solution set is obtained by translating the solution set of Ax = 0. So the solution set of Ax = b is a single vector if and only if the solution set of Ax = 0 is a single vector, and that happens if and only if Ax = 0 has only the trivial solution.

C. Since Ax = b is inconsistent, then the solution set of Ax = 0 is also inconsistent. The solution set of Ax = 0 is inconsistent if and only if Ax = 0 has only the trivial solution.

D. Since Ax = b is consistent, then the solution is unique if and only if there is at least one free variable in the corresponding system of equations. This happens if and only if the equation Ax = 0 has only the trivial solution.

Answer:

Option B: Since Ax = b is consistent, its solution set is obtained by translating the solution set of Ax = 0. So the solution set of Ax = b is a single vector if and only if the solution set of Ax = 0 is a single vector, and that happens if and only if Ax = 0 has only the trivial solution

Step-by-step explanation:

There are different ways of explaining this but we will explain it algebraic ally.

If Ax = b has a solution, then it can be said to be unique if and only if every column of A will be a pivot column. Now, If every column of A will be a pivot column, then it means that there are no free variables, and thus the homogeneous equation will have only the trivial solution.

Also homogeneous equations are always constant.

Thus the correct option is Option B: Since Ax = b is consistent, its solution set is obtained by translating the solution set of Ax = 0. So the solution set of Ax = b is a single vector if and only if the solution set of Ax = 0 is a single vector, and that happens if and only if Ax = 0 has only the trivial solution

You might be interested in
Using arithmetic operations, rewrite this polynomial in standard, simplest form.
dangina [55]
(3x2 + 9x + 6) − (8x2 + 3x − 10) + (2x + 4)(3x − 7)

First distribute the (2x+4)(3x-7) to get 6x2-2x-28
After this just add the like terms for all parts of the expression.
(3x2-8x2+6x2)+(9x-3x-2x)+(6+10-28)
x2+4x-12

So you answer is x2+4x-12
7 0
3 years ago
The sum of two consecutive odd integers is 28. What are the integers?
Fantom [35]
The correct option is B): "<span>Let x = 1st integer. Let x + 2 = 2nd integer.</span><span>"
Given that "The sum of two consecutive odd integers is 28."
 
Now the difference between two odd numbers is 2. So this means that one odd number has to be greater than the other by 2.

Let the smaller number be 'X' therefore the bigger number will be 'x+2' thus x + (x+2) = 28
 
therefore, x + x + 2 = 28 now we subtract "2" from both the sides
therefore, 2x = 26 now dividing throughout by 2 we get:

x = 13 therefore, x + 2 = 13+2
                                    = 15
 
therefore, the numbers are 13 AND 15</span>
4 0
3 years ago
Select each pair of functions that are inverses of each other
svlad2 [7]

Answer:

The first two choices only: A and B.

Step-by-step explanation:

The inverses are the ones with one relation having point (x,y) and the other relation having point (y,x). This most obvious when looking at points on a table or a list of points.

So the first pair are inverses because per point (x,y) on the first list you have (y,x) on the second list.

Examples:

1st list contains (-5,-9) while second list contains (-9,-5).

1st list contains (3,7) while the second list contains (7,3).

As long as (a,b) is in the first list and (b,a) is in the second or vice versa, then the pair of relations are inverses. So the first choice contains inverses.

Now lets talk about the pair of functions given in function notation.

Let's start with the first.

y=x+7

Extend the first idea more. Just swap x and y and then see after solving for y if what it equals is what g equals then f and g are inverses in the second choice.

x=y+7

Subtract 7 on both sides:

x-7=y

y=x-7

This is what g equals so the second choice is an answer.

The last choice does not contain a pair of inverses. Example: (2,3) is in the first list but (3,2) is not in the second.

6 0
3 years ago
Read 2 more answers
Miss Hill begun collecting baseball cards at the age of 10 his collection has increased in value as he was grown older if this p
vlada-n [284]
500 i think because 10x50
5 0
3 years ago
Read 2 more answers
W/4 = -8 i dont know how to get it
Vikentia [17]

Answer:

So I believe the question is asking what number divided by 4 is equal to -8.

This is the same as saying 4 times -8 equals what

x=4 times -8

x= -32

The answer is -32.

7 0
2 years ago
Other questions:
  • Simplify the expression. Write the answer using scientific notation. (4 x 10^13)^-2 -8 x 10^-26 6.25 x 10^-27 0.0625 x 10^-26 6.
    9·2 answers
  • (2m² + 6m) + (m² – 5m +7) <br>а. Зm² + m <br>b. Зm² - m +7 <br>с. m² + 11m - 7 <br>d. 3m² + m +7​
    15·2 answers
  • After working for 25 hours, Lamar made $375. After working for 40, Lamar made $600. Predict how much he would make after 10 hour
    7·2 answers
  • Solve the following formula for m v2=3Pmn
    13·1 answer
  • For what value of x is the rational expression below equal to zero x-4/(x+5)(x-1)
    8·1 answer
  • How is g(x) = (x - 1)^2 related to the graph of f(x) = x^2
    7·1 answer
  • The diagram shows a right-angled triangle.
    5·1 answer
  • A tube is being stretched while maintaining its cylindrical shape. The height is increasing at the rate of 2 millimeters per sec
    14·1 answer
  • In one study of 300 coffee drinkers and 150 non coffee drinkers, it was found that only 67 of the coffee drinkers had high blood
    12·1 answer
  • A game spinner has 8 sections, 3 red, 1 blue, 2 yellow, and 2 green. What is the probability of not spinning a green?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!