In parts ​(a) through ​(e)​ below, mark the statement True or False. Justify each answer.

​(a) In some​ cases, a matrix may be row reduced to more than one matrix in reduced echelon​ form, using different sequences of row operations.
Is this statement true or​ false?
A. The statement is false. Each matrix is row equivalent to one and only one reduced echelon matrix.
B. The statement is false. For each​ matrix, there is only one sequence of row operations that row reduces it.
C. The statement is true. It is possible for there to be several different sequences of row operations that row reduces a matrix.
D. The statement is true. The echelon form of a matrix is always​unique, but the reduced echelon form of a matrix might not be unique.

Answers

Answer 1

Answer:

The correct option is option A

A. The statement is false. Each matrix is row equivalent to one and only one reduced echelon matrix

Step-by-step explanation:

The matrix in echelon form is not in a unique form, as such row reduction can yield an infinite amount of answers. However a row reduced echelon form is unique and will give the same answer in every order that the row operation is performed

The statement is false. Each matrix has only one unique row echelon form, therefore, the correct option is option A.


Related Questions

Math help pls all 4 questions please

Answers

a. 32500
b. 60,400
c. 2.4 x 10 ^ -6
d. 1.47 x 10 ^3

Answer:

a)32500

b)0.00604

c)2.4×10^6

d)1.47x10-³

Step-by-step explanation:

plz can i get brainliest:)

Find the area for this problem

Answers

Answer:

63 for the whole figure, for the different shaded regions it goes as follows, 17.5 for the white area and 45.5 for the grey area

Step-by-step explanation:

The answer for the area is 68

Probability of impossible event is ………… [. ]

a) 0 b) 100% c) 1 d) both b & C​

Answers

Answer:

0

Step-by-step explanation:

Plzz I asked this three times! The Functions r and s are defined as follows.
r(x)=-2x+2
s(x)=x^2+2
Find the value of s(r(2)).

Answers

Answer:

s(r(2)) = 6

Step-by-step explanation:

You would first solve for r(2). You then input r(2) which equals -2 into s(r(2)).

r(x)= -2x + 2

r(2)= -2(2) + 2

r(2)= -4 +2

r(2)= -2

s(x)=x² + 2

s(r(2)) = (-2)² +2

s(r(2)) = 6

Simplify fully4xy/12x2y​

Answers

Answer:

1/3x

Step-by-step explanation:

for 4xy/12x^2y we need to simply one of the x's and the y's and divide both parts by 4

so we get:

1/3x

A bag contains 25 kg of flour. A baker used 80% of it to bake bread. How much flour,in kg,remained ?​

Answers

Answer:

5 kg flour remains

Step-by-step explanation:

80% of the original 25 kg comes to 0.80(25 kg), or 20 kg.  We convert 80% to its decimal equivalent, 0.80, to get this result  

The amount of flour remaing is then (1.00 - 0.80)(25 kg), or 0.20(25 kg) = 5 kg.

5 kg flour remains.

Answer:

25 - 20 = 5 kg

Steps:

25×80/100 = 25×8/10 = 200/10 = 20 kg

25 - 20 = 5 kg

Kayla invested $88,000 in an account paying an interest rate of 8 % compounded
daily. Sadie invested $88,000 in an account paying an interest rate of 8 %
compounded quarterly. After 16 years, how much more money would Sadie have in
her account than Kayla, to the nearest dollar?

Answers

Answer:

$21847

Step-by-step explanation:

Please help Z and Y

Answers

Answer:

10=Z and 10=Y

Step-by-step explanation:

since it is a 45, 45, 90 triangle

both Z and Y will be the same length

the hypotenuse has a length of [tex]x\sqrt{2}[/tex] with x being the length of the legs

Since the length of this triangle's hypotenuse is [tex]10\sqrt{2}[/tex] the side length would be 10

Hope that helps :)

The volume is 120.9 in. What is the missing dimension (X)

Answers

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Answer: x = 2.5

Explanation:

5.2 * 9.3 * x = 120.9

120.9 / 5.2 = 9.3 * x

23.25 = 9.3 * x

23.25 / 9.3 = x

x = 2.5

I hope this helped!

<!> Brainliest is appreciated! <!>

- Zack Slocum

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

What is the slope of the line that passes trough the points (-6,3) and (4,8)

Answers

Answer:

Step-by-step explanation:

Which graph can be used to find the solution(s) to x2 – 1 = 3?

Answers

We have to find the graph that can be used to find the solution of :x2 -1=3

We are given an inequality we can equate this equality to a new variable 'y' such that:x2 -1 =3=y

i.e. we get a system of equations as:y=x2-1

and y=3
Hence, the solution will be the x-value of the point of intersection of the system of equations.
The point of intersection are:
(-2,3) and (2,3).
Hence, the solution of the equation is:
x=2 and x= -2.

Hence, the solution of the equation is:
x=2 and x= -2.

Answer: D

Step-by-step explanation:

right on edge

Can anyone help me with this math equation?

Answers

Answer:

yes I can help you. the answer to the problem is 4/35.

Step-by-step explanation:

1. convert any mixed number into fractions.

your equation becomes 4/7÷5/1. this equals 4×1 over 7×5. multiply normally and your result is 4/35

Can someone help me with this. Will Mark brainliest.

Answers

I’m like 99.9% sure it’s true
it’s true ! i’m pretty sure!

There are 486 hamsters at a private showing of a new documentary about humans. If there are 12 seats in each row, about how many rows will the hamsters fill? Choose the best estimate.
A. 20
B.4
C.40
D.60

Answers

Answer:

C, 40

Step-by-step explanation:

If there are 12 seats in each row, and 486 hamsters total, then we can safely assume one hamster takes up one seat.

To find out how many rows they can take, we need to divide the number of hamsters by the number of seats to get 486 / 12 approximately equals 40.

Answer:

C.

Step-by-step explanation:

Take the first two numbers of 486.

How many times does 12 fit into 48?

4 times.

Since all of the estimations do not have any form of individual single digits (as they do normally), we would dismiss the 6 and use its place just as a '0.'

40.

Hope this helped!

PLEASE HELP QUICK WILL MARK BRANLIEST

Answers

Answer:

A, C, and B. In that order

You won the​ lottery!! You decide to first buy the expensive car​ you've always loved. There are lots of options. In addition to deciding whether you want an automatic or manual​ transmission, you have to choose an exterior color from 15​ options, an interior color from 12​ options, seats that have either a heating or massage​ option, 4 different types of audio​ systems, and 5 luxury packages with special extras for your car. If you pick one in each​ category, how many different car packages are​ there?

Answers

2(automatic/manual)x 15! (Ex Color)x 12!(int color)x 2(heat/massage)x 4!(audio)x 5!(packages)= 7210000000000000000000000

Describe the horizontal cross section of the triangular pyramid.

A.triangle
B.rectangle
C.trapezoid
D.square​

Answers

The cross section of this object would be A. Triangle

Find the output, yyy, when the input, xxx, is 303030. y = 14-0.5xy=14−0.5xy, equals, 14, minus, 0, point, 5, x y=y=y, equals

Answers

Answer:

Output, y = -1 when input, x = 30

Step-by-step explanation:

Given equation:

y = 14 - 0.5x

Where,

y = output

x = input

Find the output, y, when the input, x, is 30

y = 14 - 0.5x

y = 14 - 0.5(30)

y = 14 - 15

y = -1

Therefore,

Output, y = -1 when input, x = 30

Answer:

-1

Step-by-step explanation:

KHAN ACADEMY :)

I CAN FIND AN EXPLANATION IF NEEDED

Length of TV is 12π in. The diameter is?

Answers

Answer:

Diameter = 54 units

Step-by-step explanation:

Given:

Angle θ = 80'

Length of arc TV = 12π

Find:

Diameter

Computation:

Length of arc = [θ/360][2πr]

So,

12π = [80/360][2πr]

54 = 2r

r = 27

Diameter = 2r

So,

Diameter = 54 units

In AABC, what is AB to the nearest tenth?

Answers

Answer:

AB = 9.5 units

Step-by-step explanation:

Here, we want to find the measure of AB

To do this, we are going to make use of the sine rule

for the sine rule, the ratio of the measure of a side and the sine of the angle that faces the side is a constant value for a triangle

Thus, we have it that; in a triangle ABC

a/sin A = b/sin B = c/sin C

using the triangle given;

we need the measure of the angle at C

The sum of angles in a triangle is 180

thus;

C + 93 + 48 = 180

C = 180 - 93 -48

C = 39 degrees

Now, to get the value of AB;

AB/sin 39 = 15/sin 93

AB = (15 * sin 39)/sin 93

AB = 9.5 units

Explain how to use the standard normal table to find the probability associated with the shaded area under the curve

Answers

Answer:

to find the area to the right positive z-score begin by reading off the area in the standard mormal distribution table, since the total area under the bell curve is 1 we subtract the area from the table from 1. for example the area to the left of z=1.02 is given in the table as 0.846

Step-by-step explanation:

right answer

You like to watch movies at the local theater. You have two payment options. Your first option is to buy a discount card which will cost you $160, and then $20 for m movies, 20m + 160. Your second option will cost you $100, and then pay $40 for m movies, 40m + 100. After how many movies will the total costs of the two options be the same?

Answers

You like to watch movies at the local theater. You have two payment options. Your first option is to buy a discount card which will cost you $160, and then $20 for m movies, 20m + 160. Your second option will cost you $100, and then pay $40 for m movies, 40m + 100. After how many movies will the total costs of the two options be the same?

the answers is 3

For every 1 litre of water used to make a medicine, 300 ml of sucrose and 750ml of saline solution are used. Express the amount of water, sucrose and saline solution needed as a ratio in its simplest form.​

Answers

Answer:

20ml : 6ml: 15ml

Step-by-step explanation:

1000 milliters is 1 liter, so we would have to convert it to the ml so that it will all be in proportion. To simplify a ratio, divide by a number they can all be divided by. In this case, it was 10 first, so it made it 100: 30: 75. Then, to simplify it more, they can all be divided by 5, which is the lowest it can be since 20: 6: 15 have no numbers in common to be divided by.

The table shows the proportional relationship between the number of computers
a company sold, x, and the profit that the company made, y. The profit, y, can be
written in terms of x, the number of computers sold: y = What expression
completes the equation?
Profit on Sales
Number of Computers Sold
Profit (dollars)
3
450
7
1050
11
1650
15
2250

Answers

Answer:

y = 150x

Step-by-step explanation:

There is a proportional relationship between number of computers sold (x) and profit generated (y)

y ∝ x

y = kx

Here, k = proportionality constant

From the table given,

At y = 450 and x = 3,

450 = k(3)

k = 150

Therefore, expression that represents the proportional relationship will be,

y = 150x

The product of -2 and a number is at most 10.

Find the possible numbers.

A. n ≥ -5
B. n < -5
C. n ≤ -5
D. n > -5

Answers

Answer:

a because 5 or less than 5 equals almost or less than 10

find x. give your answer in the simplest form

Answers

Answer:

16

Step-by-step explanation:

sin = adjacent ÷ hypotenuse.

sin 45 = x ÷ 23

0.71 = x ÷ 23

0.71 × 23 = x

x = 16.26

~ 16.

Answer:

Step-by-step explanation:

using the Pythagorean theorem     a² + b² = c²

in this triangle a = x and b = x  so   x² + x²  = c²       c is the hypotenuse

         

                 x² + x²  = c²

                   2x² = c²             since c = 23 solve for x

                     x² =  c² / 2

                     x   =  ± √(c² / 2)

                     x   =  ± √(23² /2)

                          = ± √(529 /2)            

                          = ± √(264.5)            

                          =  16.26          x can't be negative

        That is correct but it doesn't answer the question

                 x = ??? / √xx

           sin 45  = √2 / 2  which equals    x / 23

                      √2 / 2  =    x / 23

                       x =  23 (√2 / 2)

                          =  23 (√2)  / 2             divide the √2 numerator and demenator

                          =  23 (√2)/√2 / (2 / √2)

                           = 23 / (2 / √2)

Sorry I have no idea what goes in the green box

In a class of 35 students, 19 take history and
12 take economics. If 5 take both subjects,
how many take neither?​

Answers

Answer: 9

Step-by-step explanation:

If 19 students take history, 12 take economics and 5 take both:

19-5 = 14 students that take only history

12-5 = 7 students that take only economics

Therefore total number of students who either history, economics or history and economics: 14 + 7 + 5 = 26

Therefore students who take neither: 35 - 26 = 9

students who take neither: 35 - 26 = 9.

What is Subtraction?

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

here, we have,

In a class of 35 students, 19 take history and

12 take economics. If 5 take both subjects,

now,

If 19 students take history, 12 take economics and 5 take both:

19-5 = 14 students that take only history

12-5 = 7 students that take only economics

Therefore total number of students who either history, economics or history and economics: 14 + 7 + 5 = 26

Therefore students who take neither: 35 - 26 = 9

To learn more on subtraction click:

brainly.com/question/2346316

#SPJ2

In ABC, mC = 30 and a = 8. If the area of the triangle is 12, what is the length of side b?
show work pls

Answers

9514 1404 393

Answer:

  b = 6

Step-by-step explanation:

The area is given by the formula ...

  Area = 1/2·ab·sin(C)

  12 = (1/2)(8)b·(1/2) . . . . . fill in the given values

  12 = 2b . . . . . . . . . . . simplify

  6 = b . . . . . . . . . . . divide by 2

The length of side b is 6 units.

(HELPP)In the figure below, AE
BD and BD bisects ∠EBC​

Answers

Answer:

7) ∠EBD = 60°

87) ∠DBC = 72°

9) ∠EBC = 156°

10) ∠EBC = 138°

Step-by-step explanation:

Please Help-
K + ⅓ = 5 ⅛ | K = ?
Show Your Reasoning.

Answers

Answer:

[tex]4\frac{19}{24}[/tex]

Step-by-step explanation:

I hope I did this right:

So first thing to do is set up the equation.

[tex]K + \frac{1}{3} = 5\frac{1}{8}[/tex]

Next thing to to is subtract 1/3 from both sides to get:

[tex]K = 5\frac{1}{8} - \frac{1}{3}[/tex]

Next up, you will multiply each of the fractions by the opposing value

(multiply 1/8 by 3 and 1/3 by 8)

[tex]K = 5\frac{3}{24}[/tex][tex]-\frac{8}{24}[/tex]

Alright almost done, by multiplying 24 by 5 you get 120, that will go in the numerator to make the math a lot easier.

K = [tex]\frac{123}{24}[/tex][tex]-\frac{8}{24}[/tex]

Finally, you subtract 123 over 24 by 8 over 24.

K = [tex]\frac{123}{24} - \frac{8}{24} = \frac{115}{24}[/tex]

Then just simplfy the 115/24 to get

[tex]4\frac{19}{24}[/tex]

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