Determine if the columns of the matrix form a linearly independent set. Justify your answer. Choose the correct answer below. A. The columns of the matrix do form a linearly independent set because the set contains more vectors than there are entries in each vector. B. The columns of the matrix do form a linearly independent set because there are more entries in each vector than there are vectors in the set. C. The columns of the matrix do not form a linearly independent set because the set contains more vectors than there are entries in each vector. D. The columns of the matrix do not form a linearly independent set because there are more entries in each vector than there are vectors in the set.

Answers

Answer 1

Th matrix is missing. The matrix is :

[tex]\begin{bmatrix}1 &-4 &4 \\ -4 &16 & 4 \end{bmatrix}[/tex]

Solution :

The column of the matrix are [tex]\begin{bmatrix}1\\ -4\end{bmatrix}[/tex] , [tex]\begin{bmatrix}-4\\ 16\end{bmatrix}[/tex], [tex]\begin{bmatrix}4\\ 4\end{bmatrix}[/tex]

Now each of them are vectors in [tex]$IR^2$[/tex]. But  [tex]$IR^2$[/tex] has dimensions of 2. But there are 3 column vectors, hence they are linearly dependent.

Therefore, the column of the given matrix does not form the [tex]\text{linearly independent set}[/tex] as the set contains [tex]\text{more vectors}[/tex] than there are entries in each vector.

Therefore, option (D) is correct.


Related Questions

The temperature at 12:00 pm was 5oF. The temperature then went down by 1.2oF every hour till 7:00 p.m. What was the temperature at 7 pm?
If you answer and show work I’ll make you brainliest pls help

Answers

Answer:

41.6 degrees (i think, sorry if it's not.)

Step-by-step explanation:

if the amount of time from 12:00 pm to 7:00 pm was 7 hours, you're going to need to take into account that you need to lower 50 degrees 7 times by 1.2 degrees. (50 - 1.2 times 7)

A ball is kicked from a height of 3 feet above ground the height of the ball is h(t) is given by h(t) = 5t raised to the 2 power +14t+3 where t is the time in seconds after the ball is kicked. How long will it take the ball to hit the ground after kicked?

Answers

Answer:

t = -2.566s and -1.169s

Step-by-step explanation:

Given the height of the ball expressed at

h(t) = 5t²+14t+3

The ball will hit the ground at h(t) = 0

Substitute and get t

0 = 5t²+14t+3

Use general formula

t = -14+/- √14²-4(5)(3)/2(5)

t = -14+/- √196-60)/10

t = -14+/- √136/10

t =-14+/- 11.66/10

t = -25.66/10 and -2.338/2

t = -2.566s and -1.169s

Hence the ball will hit the ground at these times

I GOT A 92 ON MY MATH EXAM AND I DIDN'T STUDY LETS GOOO

btw, I need help on this

if x • y = y, what are the only 2 numbers x can be?

Answers

Answer:

???

Step-by-step explanation:

x*y=y

Well, since y is on both ends of the equation, y could be 0, because anything multiplied by 0 is 0.

So x could be anything.

---

hope it helps

As a fundraiser, the Music Boosters wrapped gifts at the mall one weekend.
Out of the 100 gifts they wrapped, 310 were for weddings, and 37100 were for baby showers.
The rest of the gifts were for birthdays. What fraction of the gifts was for birthdays?
Enter your answer in the boxes.

Answers

Step-by-step explanation:

[tex]but : \\ (36790 - x) + x + (37100 - x - B) = 37100 \\ 73890 - x - B = 37100 \\ x + B = 36790 - - - (a) \\ and : \\ (310 - B - x) + x + (36790 - x) = 310 \\ 37100 - B - x = 310 \\ x + B = - 36790 \\ B = 36790 - x[/tex]

Answer:

(36790−x)+x+(37100−x−B)=37100

73890−x−B=37100

x+B=36790−−−(a)

(310−B−x)+x+(36790−x)=310

37100−B−x=310

x+B=−36790

B=36790−x

Step-by-step explanation:

good luck

Give the most precise selection
for the quadrilateral with the
following vertices.
P(0,0), Q(0,2a), R(2a,2a), S(2a,0)
A. Parallelogram
B. Rectangle
C. Square
D. Rhombus

Answers

Answer:

Its definitley square to be precise so that's my answer, but its also a rhombus

Step-by-step explanation:

assuming a is 1, regardless, graph would always be square, which is a rhombus. hope  square is correct :)

ASAP
-WILL MARK BRIANIST

Answers

Answer:

The answer is 699...............

Answer:

699

Step-by-step explanation:

First replace the value k to 12.

So our new expression will be:

3+(71-13) times 12

You first do the  Parentheses so substract  71 minus 13 which gives you 58 then multiply 58 times 12 which gives you 696 then add 3 to it and you get 699.

Fuel efficiency, measured in miles per gallon, is a measure often considered by shoppers looking for a new car. The scatterplot shows the vehicle weight of 15 car models in pounds, plotted against their highway fuel efficiency. How would the value of the correlation coefficient change if the car weights were recorded in kilograms, rather than pounds?

Answers

Answer:

There will be no change

Step-by-step explanation:

The correlation Coefficient is a measure used in regression studies to examine the strength and type of relationship which exists between two variables (dependent and independent). The Coefficient gives a negative and positive values for negative and positive relationships respectively. The correlation Coefficient has no units and hence does not depend on the unit if measurement. Therefore. Changing the unit if measurement of a certain variable, will have no effect on the correlation Coefficient.

how do you friend someone

Answers

Answer:

you gotta find a common ground.

Step-by-step explanation:

easiest way to make friends is to relate to people with experiences you share together :)

If your talking about how to friend someone on brainly: Go to the profile of the individual you'd like to invite and press on the Add Friend button and a request will be sent to them.

I hope this helps you make more friends!

Points Points Points

Answers

Yesyesyes thank you have an amazing day!

Answer:

THANK YOU!

Step-by-step explanation:

Write each quadratic expression in standard form. Draw a diagram if needed.
(x+4)(x-1)

Answers

Answer:

The standard form of the quadratic equation is x² + 3·x - 4 = 0

Step-by-step explanation:

The standard form of a quadratic equation is a·x² + b·x + c = 0

Given that the expression of the quadratic equation is (x + 4)·(x - 1) = y, we can write the given expression in standard form by expanding, and equating the result to zero as follows;

(x + 4)·(x - 1) = x² - x + 4·x - 4 = x² + 3·x - 4 = 0

The standard form of the quadratic equation is x² + 3·x - 4 = 0

The graph of the equation created with MS Excel is attached

Evaluate 2n-6+5k/3(n-9) when n=4 and k=12​

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\textsf{If n = 4 and k = 12 the substitute it into the given equation.}[/tex]

[tex]\mathsf{\dfrac{2(4) - 6+5(12)}{3(4-9)}}[/tex]

[tex]\mathsf{2\times4=\boxed{\bf 8}}[/tex]

[tex]\mathsf{\dfrac{8-6+5(12)}{3(4-9)}}[/tex]

[tex]\mathsf{8-6=\boxed{\bf 2}}[/tex]

[tex]\mathsf{\dfrac{2+(5)(12)}{3(4-9)}}[/tex]

[tex]\mathsf{5\times12=\boxed{\bf 60}}[/tex]

[tex]\mathsf{\dfrac{2+60}{3(4-9)}}[/tex]

[tex]\mathsf{2+60=\boxed{\bf 62}}[/tex]

[tex]\mathsf{\dfrac{\bold{62}}{3(4-9)}}[/tex]

[tex]\mathsf{4 - 9=\boxed{\bf -5}}[/tex]

[tex]\mathsf{\dfrac{62}{3(-5)}}[/tex]

[tex]\mathsf{3\times-5=\boxed{\bf -15}}[/tex]

[tex]\mathsf{\dfrac{62}{\bf -15}}[/tex]

[tex]\boxed{\boxed{\large\textsf{Answer: }\mathsf{\bf -\dfrac{62}{15}}}}\huge\checkmark[/tex]

[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Help please it will mean so much thanks ❤️

Answers

Answer:

y = 14

Step-by-step explanation:

y = x^2 -5x

Let x =7

y = 7^2 -5*7

y = 49- 35

y = 14

HELP I HAVE 20 MINUTES!!!!!!!!!

At Shoe Line, there are 132 boots, which make up 24% of the shoes in the store. At Shoe Warehouse, there are 120 boots, which make up 15% of the shoes in the store.
Which store has more shoes? Justify your answer by showing your work or the strategy you used.

Answers

Answer:

Shoe warehouse

Step-by-step explanation:

24% of ____ is 132

15% of ____ is 120

first lets solve what there is at shoe line. since 24% times something is 132, something is 132/24%. Since % means out of 100, do 132/24*100 is 550.

Next we do the same thing to get 120/15 * 100 = 800. So, there are more at shoe warehouse.

hope this helped, and brainliest would be appreciated :)

how many seconds are in a whole week?!
A. 200,400
B. 406,800
C. 604,800
D. 605,800
E. 604,000​

Answers

Answer:

E 604,000

Have a nice day

Solve for x. Show your work.

Answers

Answer:

x=6

Step-by-step explanation:

The sum of the angles is a right angle, which is 90 degrees

5x+ x+54 = 90

Combine like terms

6x+54 = 90

Subtract 54 from each side

6x+54-54 = 90-54

6x = 36

Divide each side by 6

6x/6 = 36/6

x= 6

no one has answered this one

Answers

Answer:

[tex]\displaystyle x = \frac{25\sqrt{2}}{2}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right  

Equality Properties

Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of Equality

Trigonometry

[Right Triangles Only] SOHCAHTOA[Right Triangles Only] cosθ = adjacent over hypotenuse

Step-by-step explanation:

Step 1: Define

Identify variables

Angle θ = 45°

Adjacent Leg = 25

Hypotenuse = x

Step 2: Solve for x

Substitute in variables [cosine]:                                                                   [tex]\displaystyle cos(45^\circ) = \frac{x}{25}[/tex][Multiplication Property of Equality] Multiply 25 on both sides:                 [tex]\displaystyle 25cos(45^\circ) = x[/tex]Rewrite:                                                                                                         [tex]\displaystyle x = 25cos(45^\circ)[/tex]Evaluate:                                                                                                         [tex]\displaystyle x = \frac{25\sqrt{2}}{2}[/tex]

Find the value of x in the triangle shown below.
х
53°
2
97°

Answers

Given:

Consider the below figure attached with this question.

To find:

The value of x.

Solution:

Angle sum property of a triangle: According to this property, the sum of all interior angles of a triangle is 180 degrees.

Using the angle sum property of triangle, we get

[tex]x^\circ+53^\circ+97^\circ=180^\circ[/tex]

[tex]x^\circ+150^\circ=180^\circ[/tex]

[tex]x^\circ=180^\circ-150^\circ[/tex]

[tex]x^\circ=30^\circ[/tex]

Therefore, the value of x is 30 degrees.

need help yet again pls and ty​

Answers

Answer:

72 I think

Step-by-step explanation:

whats the missing leg?

Answers

Answer:

Step-by-step explanation:

using pythagoras theorem

a^2+b^2=c^2

a^2+2^2=7^2

a^2+4=49

a^2=49-4

a^2=45

a=[tex]\sqrt{45}[/tex]

a=3[tex]\sqrt{5}[/tex]

a=6.7

Guys that true?
when you’re dividing do you put the bigger number first and then the smaller one or the opposite because you get different answers

Answers

Answer:

it's true for example 10/5=2 or 5/10=0.5

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

You can divide any way you want but commonly you put the bigger number in front.

Step-by-step explanation:

Antony purchases his Play Station 5 for $1,099 from Best Buy near the Parks Mall. The sales tax is 8.25%. How much does he pay for taxes? (Round to the nearest hundredth place

Answers

Answer: $90.67

Step-by-step explanation:

Sales taxes are paid per good purchased to the IRS and are more often than not, collected at the point of sale by the seller.

The sales tax paid on the PlayStation can be calculated by the formula:

= Price of purchase * Sales tax percentage

= 1,099 * 8.25%

= $90.67

Mr. Kurris is 50 years old. In four years, his house will be paid off and his daughter will be finished with collage. He wants to take out a five-year level-term life insurance policy with a face value of $750,000. The monthly premium is $61.

Answers

Complete question is;

Mr. Kurris is 50 years old. In 4 years, his house will be paid off and his daughter will be finished with college. He wants to take out a 5-year level-term life insurance policy with a face value $750,000. The monthly premium is $61,

a. What will be his total cost for this policy over the 5-year period?

b. If he dies after paying for the policy for 16 months, how much will the insurance company pay his beneficiaries?

c. If he does not die during the 5 years, how much does the insurance company make on this policy?

d. If he dies after paying for the policy for 13 months, how much will the insurance company lose on this policy?

Answer:

A) $3660

B) $750000

C) $3660

D) $749,207

Step-by-step explanation:

A) Since he wants to take out a five-year level-term life insurance policy, then number of payments for 5 years is;

12 months × 5 = 60 payments.

Since monthly premium is $61, then total cost = 61 × 60 = $3660

B) This is a level-term life insurance policy and so he will be paid the same amount over the entire period of the insurance policy.

Thus If he dies after paying for the policy for 16 months, his beneficiaries will still be paid same $750000

C) if he does not die during the 5 years, the amount the insurance company will make is same as the amount he is due for his premium which is $3660.

D) If he dies after paying for the policy for 13 months, amount that the insurance company will lose is;

>> 750000 - 13(61) = $749,207

Sophie spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -8.6°F. Between 9am and noon, the temperature rose 4.7°F. Between noon and 3pm, the temperature dropped 13.7°F. Between 3pm and 6pm, the temperature went down 14.1°F. What was the temperature at 6pm?

Answers

Answer:

Step-by-step explanation:

I have the same question :(((

sry

Susysyshdh xhdudhdh do xhxg xhxgx

MARKING BRAINLIEST AND +50 PTS IF CORRECT!!!!

(02.01)The figure shows a pair of parallel line segments on a coordinate grid:

I added the pic.

The line segments are translated 2 units to the right to form E'F' and G'H'. Which statement describes E'F' and G'H'?

Line segments E'F' and G'H' do not intersect and are closer together than EF and GH.
Line segments E'F' and G'H' intersect at (−2, 0) and are two times farther apart than EF and GH.
Line segments E'F' and G'H' intersect at (0, −2) and are two times closer together than EF and GH.
Line segments E'F' and G'H' do not intersect and are the same distance apart as EF and GH.

Answers

Answer:If you have two parallel lines and shift both to the left by the same amount, that does not alter the distance between the lines. Thus, c is correct.

Step-by-step explanation:

If the square root of n = 3/2, what is the negative square root of n ?

Answers

Answer:

use math.way

Step-by-step explanation:

has the answers


Which of the following pairs of lines are not parallel?

Answers

Answer: Not sure

Step-by-step explanation: A is wrong because they are parallel in one is on the top to the right and 1 is on the bottom. sorry thats all i know :(

Help with this one please

Answers

Answer:

v= 2

Step-by-step explanation:

[tex]6(5 - 8v) + 12 = -54\\30 - 48v + 12 = -54\\- 48v = - 54 - 30 - 12\\-48v = -96[/tex]

[tex]v = \frac{-96}{-48} = 2[/tex]

Answer:

[tex]6(5-8v)+12=-54[/tex]

[tex]=30-48v+12=-54[/tex]

[tex]=-48v=-54-12-30[/tex]

[tex]-48v=-66-30[/tex]

[tex]-48v=-96[/tex]

[tex]-v=-96/48[/tex]

[tex]v=2[/tex]

-----------------------

hope it helps...

have a great day!!

HELP!!! Due in 20 minuets

Answers

the one you have selected is right

Answer:

the one you have selected is right

Step-by-step explanation:

Kailey plays video games for x hours a month. Trent plays video games four hours more than Kylie and Megan plays two times more than Trent. Which expression relates the amount of time Megan spends playing video games?

Answers

Answer:

8 + 2x

Step-by-step explanation:

Given that :

Kyle's game time = x

Trent's game time = 4 hours more than Kylie = 4 + x

Megan's game time = 2 times more than Trent ; this equals ; 2 * (4 + x) = 2(4 + x) = 8 + 2x

What is the value of x?

Answers

Answer:

if we are finding the perimeter it would be x = 24

but if it is area it would be x = 480

Step-by-step explanation:

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