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

help me plzz pllz help now im on a time line​

Answers

Answer:

Oki, mizuki here to help!

Hi there user, looks like you need help!

Anyways, option B is the correct answer!

Step-by-step explanation:

How to find average speed: distance/time

Since the graph shows 480 meters in 6 seconds, option B should be the correct answer!

Hope this helped!

Step-by-step explanation:

we know that

Speed = Distance/ Time

so the correct answer is B

sadie travels through two intersections with traffic lights as she drives to work. The traffic lights operate inependently. The probability that both lights will be red when she reaches them is 0.22. The probability that the first light will be rerd and the second light will not be red is 0.33. what is the probability that the second light will be red when she reaches it

Answers

Answer:

The probability that the second light will be red when she reaches it is 0.4

Step-by-step explanation:

Given the two events are independent

Hence, the probability of both the red light is (P1) * (P2) = 0.22

The probability of first light being red = probability of both the intersections to have red light + probability that the first light will be rerd and the second light will not be red

probability of first light being red =  0.22 + 0.33 = 0.55

(P1) * (P2) = 0.22

Substituting the given values, we get -

0.55 * P2 = 0.22

P2 = 0.4

Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

24

Step-by-step explanation:

You need to plug in 3 for all of the x-values

That looks like 2(3)^2 + 5(3) - 9

Then if you simplify it is 2(9) + 15 - 9

Then simplify one last time and you get a final answer of 24

[tex]_____________________________________[/tex]

ANSWER:x - intercept:

[tex] \\ \tt ( - \frac{ 5 \sqrt{97} }{4} ,0),( - \frac{5 + \sqrt{97} }{4} ,0)[/tex]

y - intercept

[tex]\tt(0, - 9)[/tex]

[tex]_____________________________________[/tex]

꧁____YunaKoharuChan____꧂

Factor completely 2n + 13n + 15

Answers

Hey there!

“Factor completely 2n + 13n + 15”

2n + 13n + 15

COMBINE your LIKE TERMS

(2n + 13n) + (15)

2n + 13n = 15n

15 = 15

Answer: 15n + 15

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

15(n + 1)

Step-by-step explanation:

Given

2n + 13n + 15 ← collect like terms

= 15n + 15 ← factor out 15 from each term

= 15(n + 1) ← in factored form

What is the answer to this?

Answers

Answer:

35.4

is the answer to this question

The following are the ages of the children in your neighborhood playschool. 1, 5, 4, 8, 2, 5, 10

1. What is the MEAN age of the children in your neighborhood playschool?​

Answers

Answer:

Hi there, the correct answer should be...

The mean age of the children is 5.

Step-by-step explanation:

mean:average

1 + 5 + 4 + 8 + 2 + 5 + 10 = 35

35 ÷ 7 = 5

I need to know how to do this

Answers

Answer:

Let's walk through the steps together!

Step-by-step explanation:

1

a) we know that the Pythagorean theorem is a^2+b^2=c^2

a^2+b^2=c^2 means that if we add the squared values for each of the two sides of the triangle (these sides need to have an angle of 90 degrees together. Basically they are the ones that aren't the hypotenuse) we get the value of the hypotenuse (the longest side that doesn't help to make the right angle).

We see that we have the values of a and b in this formula (these sides need to have an angle of 90 degrees together.) Plugging the values in problem 1a into this formula, we see that 16^2+12^2=x^2 (x is the value we need to find)

16^2=236

12^2=144

so the formula now says that 236+144=x^2

236+144=400, so x= [tex]\sqrt{400}[/tex] , which is 20.

so x=20

b) we can use the same knowledge we used in the first problem in this problem as well. In this problem, we are given the values of c (the hypotenuse) and one of the sides (which for our purposes can be a).

a^2+b^2=c^2     ->      100+b^2=289

This means that b=[tex]\sqrt{289-100}[/tex]

so b=[tex]\sqrt{189}[/tex]

so b=[tex]3\sqrt{21}[/tex]

2

These ones are pretty basic, having any common knowledge of ratios should lead you right to the answer. I will help you with a and d

a) we are given the values 6 and 9 as a ratio, which is the same as a 2:3 ratio. 12 corresponds to 6, so 12 would be the 2 in 2:3, meaning the answer (for the value of x) is 18

d) we are given the values 6 and 8, and the corresponding value to 8 is 12. 6 and 8 make a ratio of 3:4, and if we plug 12 in as the 3, the 4->4*4=16

3

I can't see the full problem so unfortunately, I cannot help you

I hope this helped in your understanding!

-Suvi

Erika's first and second quarter grades are shown below. What grade does she need in
math in order to have an overall average equivalent to the first quarter? Write your answer
in the box.

Answers

Answer:

She would need an 83 in math if she wants to have an overall average equivalent to the first quarter . Tell me if im wrong

Step-by-step explanation:

please please help!! i don’t know how to do this

Answers

Answer:

What is your question I will not see and understand

Amanda bought 2 CDs that were each the same price. Including sales tax, she paid a total of $29.80. Each CD had a tax of $1.10 . What was the price of each CD before tax?
brainliest

Answers

Answer:

13.80 there you go buddy

Which expressions simplify to 2x - 3?

Answers

Answer:

-5

Step-by-step explanation:

x=-3-2

x=-5

+2 GOES ON RIGHT AND IT BECOMES -2 And then -×-is=+but 3 is greater so the sign becomes-


Credit becomes a problem when

A. banks begin to issue their own credit cards

B.credit is used to pay for things like college tuition

C.credit card companies offer people additional credit cards

D. a person cannot find the money to pay their monthly bills
Clear answer

Answers

Answer:

D. a person cannot find the money to pay their monthly bills

PLEASE HELP WITH STEPS SOLVE IN SCIENTIFIC NOTATION WILL GIVE BRAINLIEST

Answers

Answer:

use this <3 (helps calculate scientific notation) https://www.calculatorsoup.com/calculators/math/scientific-notation-converter.php

Step-by-step explanation:

​HURRY PLEASE!!!!!! Boden's account has a principal of ​$300 and a simple interest rate of ​4.4%. Complete the number line. How much money will be in the account after 4​ years, assuming Boden does not add or take out any​ money?

Answers

Answer:

$66.00

Step-by-step explanation:

first we need multiply :D I will use the formula I =prt

principal= $500

rate=3.3%

time= 4 years

but we need to convert the percent, 3.3%, to a decimal

3.3%=0.033 or .033

now we multiply !

500 × 0.033 × 4 = 66 = $66.00

(PLEASE HELP) 17. Jon read 3/8 of a book the
first day. 1/3 the second day.
and 1/4 the third day. On the
fourth day he finished the book.
What part of the book did Jon
read on the fourth day?

Answers

Answer:

[tex]\frac{1}{24}[/tex]

Step-by-step explanation:

24 is a common multiple so ill just use that as a denominator:

3/8 = 9/24

1/3 = 8/24

1/4 = 6/24

so then adding those up:

[tex]\frac{9}{24}[/tex] + [tex]\frac{8}{24}[/tex] + [tex]\frac{6}{24}[/tex] = [tex]\frac{23}{24}[/tex]

then whats left is 1/24 left to read, which cant be simplified so [tex]\frac{1}{24}[/tex]

Answer:

   [tex]\frac{1}{24}[/tex]

Step-by-step explanation:

Let x be the part of the book he read on fourth day.

[tex]\frac{3}{8} + \frac{1}{3} + \frac{1}{4} + x = 1[/tex]

[tex]LCM \ of \ 8, 3 , 4 = 24.\ Therefore , \\\\[/tex]

[tex]\frac{3}{8} + \frac{1}{3} + \frac{1}{4} + x = 1\\\\\frac{9 + 8 + 6 + 24x}{24} = 1\\\\23 + 24x = 24\\24x = 1\\x = \frac{1}{24}[/tex]

[tex]On\ the\ fourth\ day\ he\ read\ \frac{1}{24} \ of\ the\ book\ to\ finish\ it.[/tex]

does anyone have flvs geometry?​

Answers

Answer:

Step-by-step explanation: I don't

Answer:

yes

Step-by-step explanation:

I do

Aline read a report saying 39% of teachers in the United State were members of a labor union. She wants to test whether this holds true for teachers in her state, so she is going to take a random sample of teachers and see what percent of them are members of a union. Let p represent the proportion of teachers in her state that are members of a union. Write an appropriate set of hypotheses for her significance test.

Answers

Answer:

H0: p= 0.39   vs    Ha: p ≠ 0.39

Step-by-step explanation:

She wants to test whether this holds true for teachers in her state.

The test is the formulated into the hypotheses.

The null hypothesis would be

H0: p= 0.39   against the claim    Ha: p ≠ 0.39

The null hypothesis tells that the the proportion of teachers in her state that are members of a union is equal to the proportion of teachers in the US that are members of the labor union.

against the claim

That the the proportion of teachers in her state that are members of a union is  not equal to the proportion of teachers in the US that are members of the labor union.

The radius of a cylinder is equal to its height, and it has a total
surface area of 500 cm?. Find its height.

Answers

Answer:

250

Step-by-step explanation:

Divide the half from the surface area formula and it will give you the correct answer

Solve the equation below. Show all your steps

5x−8=17

Answers

5x=17+8
5x=25
X=25/5
X=5

Answer:

x=5

Step-by-step explanation:

Add 8 on both sides first. Then divide both sides by 5 to isolate the variable.

5x-8=17

add 8 to both sides

5x=25

divide by 5 on both sides

x=5

The diagonal of a rectangle is 25 in. The width is 15 in. What is the area of the rectangle

Answers

Here is your answer > >

Width of rectangle =15 inches

Length of rectangle =?

Diagonal of rectangle = 25 inches

We know that

(Diagonal of rectagle)^2=length^2+breadth^2

(25)^2=l^2+(15)^2

625=l^2+225

l^2=625-225

l^2=400

l=Root 400

l=20 inches

Hope it helps!

Thankyou ☆ ☆

Bebrainly

what are m4 and m1.............................................

Answers

Answer:

m<1 = 136

m<4 = 44

Step-by-step explanation:

Exterior angle thm:

<2 + <3 = <4

4x + 2 + 5x - 3 = 8x + 4

9x - 1 = 8x + 4

9x - 8x = 4 + 1

x = 5

m<4:

8x + 4

8(5) + 4

40 + 4

44

m<1 and m<4 are supplementary (they add up to 180) so:

m<1 + m<4 = 180

m<1 + 44 = 180

m<1 = 136

please help . please and thanks ​

Answers

Answer:

3rd option

Step-by-step explanation:

Given the x- intercepts are x = - 3 and x = 5then the corresponding factors are

(x - (- 3)) and (x - 5) , that is (x + 3) and (x - 5) , then

f(x) = a(x + 3)(x - 5) ← a is a multiplier

To find a substitute (1, 8) into the equation

8 = a(1 + 3)(1 - 5) = a(4)(- 4) = - 16a ( divide both sides by - 16 )

- 0.5 = a

f(x) = - 0.5(x + 3)(x - 5)

can someone pls help

Answers

z = 13/9?? i don't really know hope i helped

Answer:

B) z = 1 4/9

Step-by-step explanation:

z - 7/9 = 2/3

z - 7/9 = 6/9

z (- 7/9 + 7/9) = 6/9 + 7/9

z = 13/9

z = 1 4/9

PLEASE HELP what is the area of this?
B. 5 in
5 in
14 in
3 in 1 3 in
14 in
5 in
5 in

Answers

so because the shape is broken down into right triangles we’ll just use the formula

A = ab/2

and because all of our “a” and “b” are the same

a = 4
b = 3

once we’ve found one triangle

A (one triangle) = 4•3/2
A (one triangle) = 6

we can multiple our answer by 4 to find the total of our whole shape

A = 6•4
A = 24

your answer is 24 in

Rewrite [tex]f(x)=(x+7)^2-9[/tex] in standard form
Quick pls

Answers

Answer: f(x)=x^(2)+14x+40

Question : find the measure of angles x and y
show your work and write a sentence staring the answer​

Answers

Answer:

x = 53°, y = 42°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 given angles from 180° for x

x = 180° - (37 + 90)° = 180° - 127° = 53°

48° + y = 90° ( subtract 48° from both sides )

y = 42°

need help yet again pls and ty​

Answers

Answer:

72 I think

Step-by-step explanation:

math and answer please than you

Answers

Answer:

6

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

C^2 = A^2 + B^2

plug in numbers

100 = 64 + B^2

36 = b^2

square

b = 6

does anyone understand this?

Answers

Answer:

Hello! answer: 80

Step-by-step explanation:

When doing the Pythagorean theorem you do...

a^2+b^2=c^2 which is just A multiplied byitself + B multiplied byitself that will equal the number that C multiplied by itself would equal then you just figure out what multiplied byitself equals that number and thats the answer so...

64 × 64 = 4096 48 × 48 = 2304

4096 + 2304 = 6400 80 × 80 = 6400 therefore c = 80 hope that helps!

Answer:

c = 80 inches

Step-by-step explanation:

The length of the hypotenuse can be found by using the following formula in which "c" is the length of the hypotenuse, and "a" and "b" are the legs of the right angles triangle.

[tex]c = \sqrt{a^{2} + b^{2} }[/tex]

[tex]c= \sqrt{64^{2} + 48^{2} } \\c= \sqrt{4096 + 2304} \\c = \sqrt{6400} \\c = 80 inches[/tex]

What is the exact circumference of the circle?
101 it
201 ft
401 ft
600 ft

Answers

Given:

The diameter of a circle = 20 feet

To find:

The exact circumference of the circle.

Solution:

We know that the radius is half of the diameter of the circle.

The diameter of a circle is 20 feet. So, the radius of the circle is 10 feet.

The circumference of the circle is:

[tex]C=2\pi r[/tex]

Where, r is the radius.

Substituting [tex]\pi = 3.14, r=10[/tex], we get

[tex]C=2(3.14)(10)[/tex]

[tex]C=(6.28)(10)[/tex]

[tex]C=62.8[/tex]

Therefore, the exact circumference of the circle is 62.8 feet.

Note: All options are incorrect.

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