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

Answers

Answer 1

Answer:

Because [tex]x = y[/tex], then the solution is unique.

Step-by-step explanation:

Given

[tex]Ax = b[/tex]

[tex]Ax=0[/tex]

See comment for complete question

Let there be two solutions x and y.

Such that:

[tex]Ax = b[/tex] and [tex]Ay = b[/tex]

Since:

[tex]Ax = Ay = b[/tex]

Then:

[tex]Ax - Ay = b - b[/tex]

[tex]Ax - Ay = 0[/tex]

This implies that:

[tex]Ax - Ay = A(x-y) = 0[/tex]

The only trivial solution is:

[tex]Ax - Ay = A(x-y) = 0[/tex]

Such that:

[tex]x -y = 0[/tex]

Then

[tex]x = y[/tex]

Because [tex]x = y[/tex], then the solution is unique.


Related Questions

Madeline is saving up to buy a new jacket. She already has $65 and can save an
additional $5 per week using money from her after school job. How much total
money would Madeline have after 5 weeks of saving? Also, write an expression that
represents the amount of money Madeline would have saved in w weeks.
Savings after 5 weeks:
Savings after w weeks:
Submit Answer
attempt 1 out of 2

Answers

Answer:

$90

Step-by-step explanation:

Answer:

90

solve after w weeks

65+5w

Step-by-step explanation:

2x + 8y=30 y=2 solve for x

Answers

Answer:

23

Step-by-step explanation:

2x+ 8(2)= 30

2x+ 16=30

2x=14

x=7

The value for x is 23

Suppose that mean retail price per gallon of regular grade gasoline is 3.53 with a standard deviation of and that the retail price per gallon has a bell-shaped distribution. NOTE: Please use empirical rule approximations for this problem. a. What percentage of regular grade gasoline sells for between and per gallon (to decimal)

Answers

Answer:

Incomplete question, but I gave a guide to solve using the Empirical Rule.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

It is also important to note that the normal distribution is symmetric. This means of the 68% of the measures are within 1 standard deviation of the mean, for example, 68/2 = 34% are between 1 standard deviation below the mean and the mean, and 34% are between the mean and 1 standard deviation above the mean.

In this question:

You take the mean and the standard deviation. Then you take both bounds that the percentage asks, and see how many standard deviations each are from the mean, and you then use the empirical rule to solve.

Which is a true statement about the transformation shown?

Answers

Answer:

B is the answer

Step-by-step explanation:

The transformation is a reflection across the y axis and you can see that they are congruent because the points are exact mirrored images.

Pls I need help I will mark Brainly

Answers

Answer:

(10⁰x 10¹ x 1¹⁰)< (10⁰ + 10¹x 1¹⁰)<(10⁰ + 10¹ + 1¹⁰)< (10 x 10¹)

Step-by-step explanation:

increasing order-

(10⁰x 10¹ x 1¹⁰)

(10⁰ + 10¹x 1¹⁰)

(10⁰ + 10¹ + 1¹⁰)

(10 x 10¹)


18. Jackie drives 160 miles from Gary, Indiana to
Indianapolis, Indiana in 4.5 hours. At that rate,
how long would it take her to drive from Gary to
Detroit, Michigan, which is a distance of 240
miles?

Answers

Answer:

11 hours and 15 minutes (11.25)

Step-by-step explanation:

make a ratio

160:4.5

240/160=1.5

so 1 and 1/2 intervals of 4.5 hours

4.5+4.5= 9

4.5/2=2.25

9+2.25=11.25

The solution is 3.75 hours

The time taken by Jackie to drive a distance of 240 miles is given by the equation A = 3.75 hours

What is Speed?

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude

Speed = Distance / Time

Given data ,

Let the equation be represented as A

Now , the value of A is

Jackie drives 160 miles from Gary, Indiana to Indianapolis, Indiana in 2.5 hours

Distance = 160 miles

Time = 2.5 hours

So , the speed = distance / time

Substituting the values in the equation , we get

Speed = 160 / 2.5

Speed = 64 miles / hour

Now , the new distance = 240 miles

So , the Time required = Distance / Speed

Substituting the values in the equation , we get

Time required A = 240 / 64

Time required A = 3.75 hours

Therefore , the value of A is 3.75 hours

Hence , the time taken with a speed of 64 mph is 3.75 hours

To learn more about speed click :

https://brainly.com/question/22228723

#SPJ2

the longest side of a triangle is 10 cm which group of the line segments could form the other two sides of the triangle

5 cm and 5 cm

7 cm and 8 cm

9 cm and 10 cm

4 cm and 4cm​

Answers

Answer:

7 cm and 8 c

Step-by-step explanation:

7 cm and 8 cm.  Why?  Because both are shorter than the longest side (10 cm) but add up to more than 10 cm.

which rectangle has an area of 36 square units​

Answers

Answer:

this sounds like a multipel choice, but you don't have any choices listed here

Step-by-step explanation:

Answer:

option 2 just took it

Step-by-step explanation:

   

Solve for the value of z.

Answers

Answer:

13°

Step-by-step explanation:

2z + 5° + 5z - 6° = 90° { being complementary angles }

7z = 90° + 1°

7z = 91°

z = 91° / 7

z = 13°

Hope it will help :)

Answer:

2z+5+5z-6=90(right angle)

7z=90+1

z=91/7=13 is your answer

2. A line that intersects two or more
lines is called a??

Answers

Answer:

Transversal

Step-by-step explanation:

by defination this is a line that intersects other lines

What is the length of the line segment below?
(107)
(3.1

Answers

Do you have a picture?

It is on the photo please answer fast really need help

Answers

Answer:

The GCF is 3x.

The factored form is 3x(2x²+3x+4)

Write the equation in slope intercept form given the following

Answers

Answer:

the first answer is: y=2x  the second answer is y=2x+10

Step-by-step explanation:

solve the equation x- 1/4 = 3/8

Answers

Answer:

x = 5/8

Step-by-step explanation:

x - 1/4 = 3/8

Add 1/4 to both sides.

x - 1/4 + 1/4 = 3/8 + 1/4

x = 3/8 + 2/8

x = 5/8

Answer:

5/8

To tell you the truth I use a calculator app

A jar contains 38 red marbles numbered 1 to 38 and 38 blue marbles numbered 1 to 38 a marble is drawn at random from the jar

Answers

Answer:

[tex]P(Red) = 0.50[/tex]'

[tex]P(Odd) = 0.50\\[/tex]

Step-by-step explanation:

Given

[tex]Red = 38[/tex]

[tex]Blue = 38[/tex]

Required (Missing part of the question)

(a) The marble is red. (b) The marble is odd-numbered

Solving (a): Probability of Red.

This is calculated as:

[tex]P(Red) = \frac{Red}{Total}[/tex]

[tex]P(Red) = \frac{38}{38+38}[/tex]

[tex]P(Red) = \frac{38}{76}[/tex]

[tex]P(Red) = 0.50[/tex]

Solving (b): Probability of Odd

Since each marble type is numbered 1 to 38, then half of it are odd.

i.e. 19 odd numbered red marbles and 19 odd numbered blue marbles.

So, the probability of odd is:

[tex]P(Odd) = \frac{Odd}{Total}[/tex]

[tex]P(Odd) = \frac{19+19}{38+38}[/tex]

[tex]P(Odd) = \frac{38}{76}[/tex]

[tex]P(Odd) = 0.50\\[/tex]

A digital music
2. service sells 12 songs
for $9.96. At this rate,
how many songs
can you purchase
for $4.15?

Answers

Answer:

You can buy 5 songs.

Step-by-step explanation:

First, you would divide 9 by 12 which is 0.83, assuming that each song costs 0.83 by itself you would just add 0.83 + 0.83 until you reach 4.15, the amount of times you added is the answer, which is 5 lolz

how do you write 52 as a power of 6

Answers

Answer:

52^6 , there u go hopw this helps ask me anything u want im always here to help

Answer:

52^6

Step-by-step explanation:

Last year at Sarah's bakery she sold 38 birthday cakes for $57 per cake . She spent 1/2 of that money on ingredients for baking the cakes . How much money did she spend on ingredients for the cakes ?

Answers

Answer: $1083

Explanation: see photo attached below

Answer:

They are right

Step-by-step explanation:

Because

They

Are !!

The difference of two numbers is 2. Their sum is 12. What are the numbers?

Answers

Answer:

the numbers would be 5 and 7.

Step-by-step explanation:

"the difference of two numbers is 2."

7 - 5 = 2

"their sum is 12."

7 + 5 = 12

since the difference of 7 and 5 is 2 and the sum of 7 and 5 is 12, 5 and 7 are the numbers that fulfill the statement.

i hope this helps! have a lovely rest of your day <3

Chick-fil-a found out their most popular items in their combo meals . They found that the Original Chicken Sandwich was ordered 65% of the time, and the grilled was ordered 20% of the time, the other 15% was other options. The fries were ordered 80% of the time and 20% of the time another side item was ordered. What is the probability that someone
orders an Original Chicken Sandwich?

Answers

Answer:

13/20 probability

Step-by-step explanation:

it starts out as 65/100 then you simplify to get 13/20

hope this helps btw chick fil a is the best!

Identify a set of parallel and a set of perpendicular lines in this image

Answers

Answer:

GHJKL

Step-by-step explanation:

VBNM,

What is tan A?
Tan A =

Answers

Answer:

5/12

Step-by-step explanation:

tan is opposite/adjacent

the opposite of a is 5 and the adjacent of a is 12

Graph the line with slope -2/3 passing through the point (-5, -1)

Answers

Answer:

The graphed line is in the screenshot below:

Write the equation of the line perpendicular to the given line that contains P.

P(-6, -3) y=x-1

Answers

Answer:

y= -x-9 because you have to find the negative reciprocal of the slope of the original line and then use the point slope formula y-y1=m(x-x1) to find the perpendicular line

Imagine that you are representing your classmates. What are their needs? What would you advocate for their behalf? Not math related

Answers

Answer:

As a former runner upper Senior Class Secretary I can say that your classmates need the following:

1. To be respected, even when others may not respect them.

2. They need a leader who can listen to what they have to say and DO SOMETHING about it.

3. They need the feeling of commitment when given the oppurtunity to improve.

4. They need rules, guidlines and restrictions.

(I would advocate that we have a strong leader....Is it going to be you?)

what did the teenage yardstick say to its parents

Answers

Answer:

I want to stand on my own three feet

Step-by-step explanation:

Ignore the bottom but can someone help me and give me the right answer please also put how you got the answer so show your work please!!!!

Answers

Answer:

4x-15

Step-by-step explanation:

5(x-3)-x

first we want to distribute 5 to x and -3

5xx=5x 5x-3=-15

now we have

5x-15 - x

then we just have to combine like terms and the only alike terms are 5x and -x

5x-x=4x

so the answer is 4x-15

Answer:

5x-15-x

4x-15is your answer

If a snowball melts so that its surface area decreases at a rate of 5 cm2/min, find the rate (in cm/min) at which the diameter decreases when the diameter is 9 cm

Answers

Answer:

0.0221 cm/min

Step-by-step explanation:

Surface area of a snowball:

An snowball has a spherical format.

The surface area of an sphere is given by:

[tex]A = 4\pi r^2[/tex]

In which r is the radius(half the diameter). So in function of the diameter, we have that:

[tex]A = 4\pi (\frac{d}{2})^2 = \pi d^2[/tex]

Implicit derivative:

To solve this question, we need to find the implicit derivative of A in function of t.

The variables are A and d, so:

[tex]\frac{dA}{dt} = 8\pi d \frac{dd}{dt}[/tex]

Its surface area decreases at a rate of 5 cm2/min

This means that [tex]\frac{dA}{dt} = -5[/tex]

Find the rate (in cm/min) at which the diameter decreases when the diameter is 9 cm

This is [tex]\frac{dd}{dt}[/tex] when [tex]d = 9[/tex]. So

[tex]\frac{dA}{dt} = 8\pi d \frac{dd}{dt}[/tex]

[tex]-5 = 8\pi*9 \frac{dd}{dt}[/tex]

[tex]\frac{dd}{dt} = -\frac{5}{72\pi}[/tex]

[tex]\frac{dd}{dt} = -0.0221[/tex]

This means that the diameter decreases at a rate of 0.0221 cm/min when the diameter is 9 cm.

Slope is 0, y-intercept is 5

Answers

Answer:

Step-by-step explanation:

This is what the graph would look like with the y intercept and the slope (p.s. I used Desmos Graphing calculator)

Graph y = -3x + 7.
2

Answers

Answer:

I love math anyways

The ans is in the picture

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation:

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