Which of the following statements are true? Remember that a mathematical statement is said to be true if it is always true, under all circumstances.
A. Every matrix equation Ax b corresponds to a vector equation with the same solution set.
B. If A is an m x n matrix and if the equation Axb is inconsistent for some b in R", then A cannot have a pivot in every row.
C. The first entry in the product Ax is a sum of products.
D. If the augmented matrix [A l b] has a pivot position in every row, then the equation Ax-b is inconsistent.
E. The equation Ax-b is consistent if the augmented matrix [A I b] has a pivot position in every row.
F. If A is an m x n matrix whose columns do not span Rm, then the equation Ax-b İs inconsistent for some b in R.

Answers

Answer 1

Answer:

A, B, C, F

Step-by-step explanation:

Statement A is true.

All the matrix equation of the order always corresponds to any vector equation having the same solution set.

Statement B is true.

If P is any matrix of the order m x n and if the equation [tex]$Px=b$[/tex]  is inconsistent for any b in [tex]$R^m$[/tex] , then P does not have a pivot in all the rows.

Statement C is true.

The first entry of elements in a product Ax is the sum of the products.

Statement F is true.

If a matrix A of order m x n and whose columns does not span  [tex]$R^m$[/tex] , then equation [tex]$Ax=b$[/tex]  will be inconsistent for any b in [tex]$R^m$[/tex] .


Related Questions

Write an Equation using the following arithmetic sequence: 5, _____, ______, -4.

Answers

Answer is 5,2,-1,-4 the reason it multiples of 3

In the following diagram, it is known that EHG is a right angle, m EHF x   1 and m GHF x    5 5.
Find the value of x, the numerical values of m EHF m GHF   and , and mark them on the diagram

Answers

Answer:

Step-by-step explanation:

From the diagram, it can be seen that  m EHF+ m GHF = mEHG

mEHG is a right angle, then mEHG = 90°

Given

m EHF = x

m GHF = 5x

Substituting the given parameters into the formula to get x;

x+5x= 90

6x = 90

Divide both sides by 6;

6x/6 = 90/6

x = 15

Hence the value of x is 15°

Since m EHF = x, therefore the numerical value of m EHF is 15°.

Also since m GHF = 5x, the numerical value of m GHF = 5(15) = 75°

Solve the equation for n

y=nx+m

N=?

Answers

n= (y-m)/x

y minus m over x

Last week, Jada ran 2 7/10 miles. This week, she plans to run 5 times as far as last week.
How many miles does Jada plan to run this week?
Write your answer as a fraction or as a whole or mixed number.

Answers

Answer:

13.5 miles or 27/5 miles

Step-by-step explanation:

2 7/10 is equal to 2.7  If she plans to run 5 times as much as last week, multiply 2.7 by 5.

2.7*5=13.5

what is the distance between -4 and 8 on a number line

Answers

Answer:

12

Step-by-step explanation:

you can hop 12 times to the right

The distance between -4 and 8 on a number line is 12.

To find the distance between -4 and 8 on a number line, you can subtract the smaller number from the larger number. In this case:

Distance = |8 - (-4)|

To subtract a negative number, you can think of it as adding the absolute value of that negative number:

Distance = |8 + 4|

Now, perform the addition:

Distance = |12|

The absolute value of 12 is 12, so the distance between -4 and 8 on a number line is 12 units.

Hence, the distance between -4 and 8 on a number line is 12.

To learn more on Distance click:

https://brainly.com/question/15172156

#SPJ6

Solve the equation. Three-fourths times x equals 9. A. x equals 12. B. x equals 108. C. x equals 72. D. x equals four-ninths.

Answers

Answer:

The answer is A.) x = 12

Step-by-step explanation:

I hope this helps!

Answer: 12

Step-by-step explanation:

ANYONE THAT IS GOOD AT PRECAL! Inbox me ill CASHAPP YOU!!

Answers

Sorry I'm not that good but I can suggest you a person... Just go friends and search demilade25... It's the exact name demilade25.. He can help you very well

Two identical pumps fill a water reservoir in 10 hours. How many additional pumps should be turned on if the reservoir must be willed in 4 hours?

Answers

Answer:

5

Step-by-step explanation:

All you have to do is 2*10=20 and then 20/4=5

So 5 additional pumps should be turned on.

The number of additional pumps that should be turned on if the reservoir must be filled in 4 hours is 3 pumps

Given:

2 identical pumps = 10 hours

Time taken for each pump = Total time ÷ number of pumps

= 10 hours / 2 pumps

= 5 hours per pump

Total hours to fill a reservoir = 4 hours

let

x = number of pumps

Number of pumps = (Time taken for each pump × Total hours to fill a reservoir) / Total hours to fill a reservoir

= (5 × 4) / 4

= 20 / 4

= 5 pumps

Additional pump needed = Pumps needed - available pumps

= 5 - 2

= 3

Therefore, number of additional pumps that should be turned on if the reservoir must be filled in 4 hours is 3

Read more:

https://brainly.com/question/20424149

What is the answer to 18-4K=-10-4k?

Answers

Answer:

  no solution

Step-by-step explanation:

add 4k to both sides of the equation and you have ...

  18 = -10  . . . .  false

There is no value of k that will make this statement true. There is no solution.

11. The first four terms of an AP, whose first term is -2 and common difference is -2 are​

Answers

Answer:

- 2, - 4, - 6, -8

Step-by-step explanation:

If the first term of the arithmetic sequence is is -2 , and the common difference is -2, then we can generate the first four terms the following way:

a1 = - 2

a2 = - 2 - 2 = - 4

a3 = - 4 - 2 = - 6

a4 = - 6 - 2 = - 8

Jhalen gave a presentation in health class about the importance of supportive sneakers. His presentation was 2/3 the length of Lenayah's presentation on medicine. Jhalen's presentation was 8 minutes. How long was Lenayah's presentation?

Answers

Answer: Lenayah's presentation was 12 minutes long.

Step-by-step explanation:

Set up a proportion. 2/3 = 8/x. Cross multiply. 2x = 24Divide both sides by 2. x =12

Which term completes the product so that it is the difference of squares?

(−5x−3)(−5x+________)

Answers

Answer:

3

Step-by-step explanation:

For Edge Users its

C

Answer: C. 3

Step-by-step explanation: Just confirming what the other person wrote :)

6. What is the fractional equivalent of 3.15?

Answers

How to Write 3.15 or 315% as a Fraction?

Decimal    Fraction              Percentage

3.3               66/20                        330%

3.25         65/20                          325%

3.2                 64/20                            320%

3.15             63/20                             315%

3.1                   62/20                               310%

3.70588   63/17                          370.588%

3.5              63/18                                         350%

3.31579       63/19                                     331.579%

3              63/21                                         300%

What is |v + 81 – 5 = 2

Answers

Answer:

-1 , -15

Step-by-step explanation:

| v + 8 | - 5 = 2

(add 5 both sides)

| v + 8 | = 7

(create two equations

v + 8 = 7          v + 8 = -7

(subtract 8 both sides)

v = -1     and    v = -15

Dmitar buys 2/3 pound of mixed nuts,1/2 pound of chocolate candies, and 1 1/4 of granola how much did dmitar spend to make the trail mix?

Answers

Answer: 11.70

Step-by-step explanation:

Lisa mixed 1 part of apple juice and 2 parts of vanilla yogurt to make a smoothie. How many parts of apple juice did Lisa mix with each part of vanilla yogurt?

Answers

Lisa mixed a 1/2 (or .5) part of apple juice with each part of vanilla yogurt.

1 divided by 2 is equal to one half (1/2 or 0.5)

Identify the independent and dependent variables in the following situation: Julie notices that her plant grows one inch for every liter of water that it receives.

Answers

Answer:

third choice the independent variable is the amount of water given, dependent is the height of the plant

-5 1/2 + 6 3/4 + ( -4 1/4)

Answers

Answer:

8

Step-by-step explanation:

I used a calculator

Three times the sum of eight and a number is 81. Find the number.

Answers

Answer:

19

Step-by-step explanation:

81/3=27

27-8=19

19

Find (9.3 × 10^6) + (1.8 × 10^4). Express your answer in scientific notation.

Answers

They answer is 9318000

Bert's birthday party will cost $246 if he invites 41 guests. How many guests can there be, at most, if Bert can afford to spend a total of $534 on his birthday party? Solve using unit rates. guests​

Answers

89 people can go if he has a budget of $534

Find x and y (round to the nearest tenths is needed)
Picture below.. help

Answers

Answer:

x=11/2

y=11√3/2

Step-by-step explanation:

This is a 30°-60°-90° triangle. So if we call the short side x, then the 2nd longest side will be x√(3), and the hypotenuse is 2x.

So here we have 11 as the hypotenuse. So:

11=2x ---> x=11/2 and y=x√3=11√3/2

You could also just take the sine and cosine of the sides using either angle as well. But this is a common ration of sides that is talked about in Math classes; especially Trig.

Edit: I missed the part where you said you wanted rounded answers. Just plug the values into a calculator and round as needed.

What's the answer to this question?

Answers

Answer: 9.4


Why?: 5+3+2= 10

You then try looking at your 5 options, and choose the one that is closest to 10. 9.4 rounds to 9, but it is closest to 10 out of all the options...


Hope this helped!

In a certain apartment building, the ratio of tenants to cars is 3:5. If there are 30 tenants, how many cars are there?

Answers

Answer:

50 cars

Step-by-step explanation: 3x10 is 30 and 5x10 is 5

You have 15 marbles in your pocket. 5 are blue, 6 are red, and 4 are green. If you reach into your pocket and pull out a marble, what is the probability that the marble will be red?

Answers

Answer:

2 out of 5 chance of being red

Step-by-step explanation:

What is 3x10,000+4x1,000+6x100+8x10+8 written in standard form?

Answers

Hello!☺

[tex]Answer:\boxed{34,688}[/tex]

[tex]Explanation:[/tex]

[tex]3*10,000+4*1,000+6*100+8*10+8[/tex]

To solve, you will need to evaluate.

[tex]3*10,000+4*1,000+6*100+8*10+8=34,688[/tex]

[tex]34,668[/tex]

Hope this helps!☺

Answer:

34,688

Step-by-step explanation:

30,000 + 4,000 + 600 + 80 + 8 = 34,688

Hopefully this helps you :)

pls mark brainlest ;)

The cost of 24 bottles of water is $6. Which expression shows how to find the cost of 10 bottles of water?

A. 24/6 x 10
B. 24/10 x 6
C. 6/10 x 24
D. 6/24 x 10​

Answers

A .
Because the cost of 24 bottles equalling 6 the equation would be 24/6 then times 10 because thats the amount of water bottles

1. Given right triangle ABC with the right angle C and sin A = 1/3, which is of the following expression is also equal to 1/3?

A. cos B
B. cos(90° - A)
C. sin(90°- B)
D. Both A and B

2. The maximum slope for a hand propelled wheel chair ramp should be a 1-inch rise to every 12 inch of length. What is that maximum ramp angle recommended to the nearest degree?

Answers

Answer:

1) B

2) About 5°.

Step-by-step explanation:

1)

We can use the following co-function identity:

[tex]\sin(\theta)=\cos(90-\theta)[/tex]

Substitute A for θ:

[tex]\sin(A)=\cos(90-A)[/tex]

Since we know that sin(A) is 1/3, this means that cos(90-A) must also be 1/3.

So, our answer is B.

2)

Refer to the drawing.

Remember that 1-inch rise is a height of 1 while a 12 inch length is a length of 12.

So, to find the maximum ramp angle, we simply need to find the value of x.

We know the sides opposite and adjacent to x. So, we can use tangent:

[tex]\tan(x)=\text{opp}/\text{adj}[/tex]

Substitute 1 for the opposite side and 12 for the adjacent side:

[tex]\tan(x)=1/12[/tex]

Take the inverse tangent of both sides:

[tex]x=\tan^{-1}(1/12)[/tex]

Use a calculator. Make sure you're in Degrees mode:

[tex]x\approx4.76\textdegree\approx5\textdegree[/tex]

So, the maximum ramp angle should be about 5°


Simplify the expression. If not possible, write simplified.
3 - 2y +9

Answers

Answer:

-2y + 12

Step-by-step explanation:

3 - 2y +9

Combine the constants

-2y +3+9

-2y + 12

Answer:

-2y + 12

Step-by-step explanation:

1) Group like terms: -2y + 3 + 9

2) Combine like terms: 3 + 9 = 12

3) -2y + 12

Hope this helps and good luck with your assignment. (pleasem mark me brainliest if possible)

1/2x+ y=-7
-3x + 2y = -2
You could produce a pair of like terms with
opposite coefficients by multiplying the first equation by what number

Answers

Answer: 6

explanation: I just did it

Answer:

Step-by-step explanation:

Answer is 6

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