Suppose Ax = b always has at least one solution no matter what b is. Why AT y = 0 has only the trivial solution y = 0?

Answers

Answer 1

Answer:

For the first equation we have:

A*x = b

solving for x, we get:

x = b/A

If it always has a solution, then we can not have A = 0, because that causes an undefined operation.

so for example, if we have A = 1 and b = 2

x = b/A = 2/1

For the other case,

A*y = 0

dividing both sides by A

y = 0/A = 0

y = 0

Here we have only one possible solution, the trivial one, y = 0.

And the dependence on A disappears (because the quotient between zero and a number different than zero is always zero)


Related Questions

There is a bag with only red marbles and blue marbles.
The probability of randomly choosing a blue marble is
There are 63 marbles in total in the bag and each is equally likely to be chosen.
Work out how many red marbles there must be.

Answers

Answer:

There might be 31 or 32

Step-by-step explanation:

I would have a better answer if i knew the probability of the blue marbles being chosen srry.

the pair of the lines x^2-3y^2=0 and the straight line x=a enclose a triangle which is

Answers

Step-by-step explanation:

x²-3y²=0x=√3y and x-√3yΔOAB is equilateral triangle∴ orthocentre and centroid of ΔOAB concides ∴ orthocentre =( 29/3 ,0)=( x1 + x2 + x3 / 3 , y1 + y2 + y3 / 3 )I NEED BRAINLIEST ✌️ PLZ

Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?

A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.

Answers

Answer:

A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.

Step-by-step explanation:

Given

[tex]3(8 - 4x) < 6(x - 5)[/tex]

Required

Describe the number line

We have:

[tex]3(8 - 4x) < 6(x - 5)[/tex]

Open brackets

[tex]24 - 12x < 6x - 30[/tex]

Collect like terms

[tex]-12x - 6x < -30 - 24[/tex]

[tex]-18x < -54[/tex]

Divide by -18 (the inequality changes)

[tex]x > 3[/tex]

[tex]>[/tex] means that the arrow on the number line points to the right, and it makes use of an open circle that starts from 3.

Answer:

based on what he said the answer is b

Step-by-step explanation:


Can any one help me with all these 3 questions? Thank you if you helped :)

Answers

8. rational, integer whole

Answer: Answer already been answered credits to that person give that person brainliest

Step-by-step explanation:

HELP ASAP PLEASE!!!!!!!

Answers

Answer:

the answer is 2

Step-by-step explanation:

it doesn't match the other  but is 2  

The outer dimensions of a closed rectangular cardboard box are 8 centimeters by 10 centimeters by 12 centimeters, and the six sides of the box are uniformly 12 centimeter thick. A closed canister in the shape of a right circular cylinder is to be placed inside the box so that it stands upright when the box rests on one of its sides. Of all such canisters that would fit, what is the outer radius, in centimeters, of the canister that occupies the maximum volume

Answers

Answer:

Vmax = 192.33 cm³

Step-by-step explanation: An error in the problem statement. The sides of the box could not be 12 cm. We assume 1.5 cm

Inside dimensions of the box:

Outer dimensions :          12          10         8

 2 *  1.5   =  3                      3            3         3

Inside dimensions:            9            7         5

The volume of a right circular cylinder is:

V(c)  =  π*r²*h              r is the radius of the base and  h the height

By simple inspection is obvious that volume maximum will occur when r is maximum, and r is maximum, only when the base of the cylinder is in the rectangle 12*10. ( Inside  dim  9*7 ) In that case r  =  7/2   r = 3.5 cm

Then the height is 5 cm.

And the maximum volume of the cylinder is:

Vmax = 3.14* ( 3.5)²*5

Vmax = 192.33 cm³

Find the size of each of the unknown angles. Help me plz​

Answers

Answer:

2a+15 = 125(being alternate angle)

or,2a = 125-15

or,2a = 110

or,a = 110÷2

,a = 55

again,2a+15+b+30=180(Being co-interior angle)

or,2×55+15+b+30=180

or,110+15+30+b=180

or,155+b=180

or,b=180-155

Therfore,b=25

A fruit punch mixture is made of Orange juice, Pineapple juice, in a 3:5:7 ratio. How much of each juice type do you need for a 375 mL mixture?

Answers

Answer:

Amount of orange juice = 75 ml

Amount of Pineapple juice = 125 ml

Amount of mix juice = 175 ml

Step-by-step explanation:

Given:

Type of juice

Orange juice, Pineapple juice, mix juice

Ratio: 3 : 5 : 7

Amount of juice mixture = 375 ml

Find:

Amount of each juice

Computation:

Let common ratio = a

So,

3a + 5a + 7a = 375

15a = 375

a = 375 / 15

a = 25

Amount of orange juice = 3a

Amount of orange juice = 3(25)

Amount of orange juice = 75 ml

Amount of Pineapple juice = 5a

Amount of Pineapple juice = 5(25)

Amount of Pineapple juice = 125 ml

Amount of mix juice = 7a

Amount of mix juice = 7(25)

Amount of mix juice = 175 ml

What is the
No solution, one solution, and infinitely solutions
to the equation 2x+5+2x+3x=3x+5?

Answers

Answer:

one solution

Step-by-step explanation:

PLEASE I NEED HELP. summer school

Answers

Answer:

1. Y+2/5y

2. y-0.32y

3. Y-2/5y

4. y+0.32y

Step-by-step explanation:

Yes what she said. She’s right

Which is the graph of y = 3x + 1 - 2?​

Answers

is there supposed to be a picture?

i need help with this problem can someone help me!!!!

Answers

Answer:

x = 3 in

Step-by-step explanation:

From the Pythagorean theorem,

x² = 4²-7²

√(4²-√7²)

= √(16-7)

= √9

= 3 in

Answered by GAUTHMATH

the school is located 0.8 miles west of willows house the park is 1.5 miles north what is the distance between willows house and the park

Answers

Answer:

0.7

Step-by-step explanation:

1.5 - 0.8 = 0.7 :)) hope u get it right!!!

The distance between the school and the park will be 0.7 miles.

What is the distance?

Distance is defined as the length between the two points just like in the question it is the length between the school and the park.

Given that:-

The school is located 0.8 miles west of willows house The park is 1.5 miles north

The distance will be calculated as:-

Distance   =   1.5   -   0.8   =   0.7 miles  

Therefore the distance between the school and the park will be 0.7 miles

To know more about distance follow

https://brainly.com/question/2854969

#SPJ2

WILL GIVE BRAINLIEST!!!

CR and DS are perpendiculars dropped from AB to PQ, and AB is perpendicular to CR and DS. If CR = DS, which statement must be true?

A. m B. m C. m D. m E. m

Answers

Answer:

The answer is C.) mRCD = mACD ÷ 2

RCD = ACD divided by two.

RCD = 90 degrees

ACD ÷2 = 180÷2 = 90 degrees.

So, your answer is C.

Hope this helped. Have a grey day!

Answer:

C. m∠RCD = m∠ACD ÷ 2

Hope this helps!

Step-by-step explanation:

I got it right.

can i please get some help on this one?

Answers

Answer:

wht yr u in tis is too hard yk

Step-by-step explanation:

Question 1 of 10 If f(x) = 5x and g(x) = x+1, find (f.g)(x).

Answers

Answer:

D

Step-by-step explanation:

(f • g)(x)

= f(x) × g(x)

= 5x³( x + 1) ← distribute parenthesis

= 5[tex]x^{4}[/tex] + 5x³ → D

Which of the following are true statements? Check all that apply. (WILL GIVE BRAINLIEST)

A. log(M/N) = (logM)/(logN) B. logM+logN=log(MN)
C. log(M/N)=logM-logN
D. logM-logN=log(M-N)

Answers

Answer:

B and C are the correct answers

Step-by-step explanation:

Hope this helps!

The statement B and C are true according to logarithm rules.

What are logarithms?

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

A) log(M/N) =log M/log N

Quotient rule is log (x/y)=log x-log y

So, which in not true

B) logM+logN=log(MN)

Product rule is log(xy)=logx+logy

So, the statement is ture

C) log(M/N) =log M - log N

Quotient rule is log (x/y)=log x-log y

So, the statement is ture

D) log M - log N=log(M-N)

Quotient rule is log (x/y)=log x-log y

So, which in not true

Therefore, the statement B and C are true according to logarithm rules.

To learn more about the logarithmic equation visit:

https://brainly.com/question/14406101.

#SPJ2

Two times the difference of a number and ten is forty two

Write an equation to represent the sentence:

Answers

Answer:

let the number be x

representing the equation...

it will be....

2 times (the number- 10)=42

2 times(x-10)= 42

2(x-10)=42

Someone please help me on this and please tell me the answer directly please !!

Answers

Answer:

0.01

0.05y-0.12y-0.06

Answer:

First one should be: 0.05 + 0.1y = 0.12 + 0.06y

Second one is 100

Step-by-step explanation: Trust me:)))

Find the values of x and y. Round your answers to the nearest tenth if necessary,

Answers

Answer:

[tex]x=12,\\y=12\sqrt{3}[/tex]

Step-by-step explanation:

In any 30-60-90 triangle, the side lengths are in the ratio [tex]x:x\sqrt{3}:2x[/tex], where [tex]2x[/tex] is the hypotenuse, or longest side, of the triangle and [tex]x[/tex] is the side opposite to the 30 degree angle.

In the given 30-60-90 triangle, the longest side (hypotenuse) is marked as 24. Since [tex]x[/tex] is opposite to the 30 degree angle,

Therefore, we have:

[tex]x=\frac{24}{2},\\x=\boxed{12}[/tex]

Based on our side length ratio [tex]x:x\sqrt{3}:2x[/tex], [tex]y[/tex] is then:

[tex]y=x\sqrt{3}\text{ for}\implies x=12,\\y=\boxed{12\sqrt{3}}[/tex]

Answer:

[tex]\huge\boxed{x=12;\ y=12\sqrt3\approx20.8}[/tex]

Step-by-step explanation:

Look at the picture.

We have:

[tex]2a=24\\a=x\\a\sqrt3=y[/tex]

Therefore:

[tex]x=24:2=12\\\\y=12\sqrt3\approx12\cdot1.73=20.76\approx20.8[/tex]

What is 600000+45 yes I'm back

Answers

Answer:

600045

Step-by-step explanation:

Answer:

Hmm the answer might be 600045

Step-by-step explanation:

So what you do is that you add them up using your calculator or brain.

write two such ratios number whose multplicativen inverse is same as they are​

Answers

Answer:

1 and -1 are two rational numbers whose multiplicative inverse is same as they are.

Step-by-step explanation:

mark me brainlist

help me please!!!!!!!!

Answers

Try using the Butterfly method

Answer:

1/2

Step-by-step explanation:

2. Estimate the square root of the following
(i) 99
(ii) 572
(iii) 11437
(4) 476
(5) 9027
(6) 512375

Answers

Answer:

1..9.9

2....23.9

3...106.9

4....21.8

Step-by-step explanation:

1-9.9

2-23.9

3-106.9

4-21.8

5-95.01

6-715.8

Mr. Chong deposits RM5 000 into a fixed deposit account with 4% interest rate compounded every 3 months for a period of 3 years. Calculate the amount of interest accrued after the third year。



fast please tq

Answers

Answer:

The interest is 634.13.

Step-by-step explanation:

Amount deposit , P = 5000

Interest, R = 4 % so, R = 4/4 = 1 %

Time, T = 3 years quarterly

n = 3 x 4 = 12

Let the amount is A.

Use the formula of the compound interest

[tex]A = P \left ( 1 + \frac{R}{100} \right )^n\\\\A = 5000 \left ( 1 + \frac{1}{100} \right )^{12}\\\\A = 5634.13[/tex]

So, the interest is

I = A - P = 5634.13 - 5000 = 634.13

Need help ASAP I will mark brainliest

Answers

Answer:

see image

Step-by-step explanation:

Ah what is the length of XB? I really need to learn how to solve this

Answers

Answer:

5.28

Step-by-step explanation:

we use the formula

H²=B²+P²

and we will get the answer

branliest if it is helpful

Answer:

Angle BXY

using pythogoras theory which is

hyp*2= opp*2 +adj*2

hypothenus being the longest part of the angle BX=?

Step-by-step explanation:

hyp= 4.2*2+ 3.2*2

hyp*2 =17.64 + 10.24

hyp*2 = 27.88

hyp =√27.88

hyp=5.28...Ans

note *2...square

∣1/12 − 5/6∣ − (2/5 + 1/10)

I WILL GIVE BRAINLYST

Answers

Answer:

forst mark me as a brainleast

Solve the following linear quadratic system of equations algebraically.

y=^2+3x-2
y+3=5x

Answers

Answer:

[tex]x=1[/tex]

[tex]y=2[/tex]

Step-by-step explanation:

[tex]y=x^2+3x-2[/tex] , [tex]y+3=5x[/tex]

Replace all occurrences of [tex]y[/tex] in [tex]y+3=5x[/tex] with [tex]x^2+3x-2.[/tex]

[tex](x^2+3x-2)+3=5x[/tex]

[tex]y=x^2+3x-2[/tex]

Add [tex]-2[/tex] and 3.

[tex]x^2+3x+1=5x[/tex]

[tex]y=x^2+3x-2[/tex]

Subtract 5x from both sides of the equation.

[tex]x^2+3x+1-5x=0[/tex]

[tex]y=x^2+3x-2[/tex]

Subtract 5x from 3x.

[tex]x^2-2x+1=0[/tex]

[tex]y=x^2+3x-2[/tex]

Rewrite 1 as [tex]1^2[/tex].

[tex]x^2-2x+1^2=0[/tex]

[tex]y=x^2+3x-2[/tex]

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

[tex]2x=2[/tex] · [tex]x[/tex] · [tex]1[/tex]

[tex]y=x^2+3x-2[/tex]

Rewrite the polynomial.

[tex]x^2-2[/tex] · [tex]x[/tex] · [tex]1[/tex] [tex]+[/tex] [tex]1^2=0[/tex]

[tex]y=x^2+3x-2[/tex]

Factor using the perfect square

trinomial rule [tex]a^2-2ab+b^2=(a-b)^2,[/tex]

where a = x and b = 1.

[tex](x-1)^2=0[/tex]

[tex]y=x^2+3x-2[/tex]

Set the [tex]x-1[/tex] equal to 0.

[tex]x-1=0[/tex]

[tex]y=x^2+3x-2[/tex]

Add 1 to both sides of the equation.

[tex]x=1[/tex]

[tex]y=x^2+3x-2[/tex]

Replace all occurrences of [tex]x[/tex] in

[tex]y=x^2+3x-2[/tex] with 1.

[tex]y=(1)^2+3(1)-2[/tex]

[tex]x=1[/tex]

[tex]y=2[/tex]

What is the slope of the line shown below?

Answers

a. negative one over six

Answer:

Hello there,

The correct answer to this question would be D 1/6

Step-by-step explanation:

I had took the test and it said it was correct.

Anyways hope this helps

if the answer is correct pls mark Brainliest

thank you, have a nice day

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