For each of the situations described below,give an example(if it’s possible) or explain why it’s not possible.

a. A set of vectors that does not span R^3. After adding one more vector, the setdoes spanR3.
b. A set of vectors that are linearly dependent. After adding one more vector, theset becomes linearly independent.

Answers

Answer 1

Step-by-step explanation:

a) If the given set of vectors does not span [tex]\mathbb{R}^{3}[/tex] , it means the number of linearly independent vectors are less than 3. So by adding one or more linearly independent vectors with respect to existing vectors, we can convert the set to basis and basis always spans vector space.

eg. [tex]S= \left \{ (1,0,0)^{T},(1,2,0)^{T} \right \}[/tex] this set does not span [tex]\mathbb{R}^{3}[/tex] . Since it has only two vectors and both vectors are linearly independent, so adding one linearly independent vector with respect to the vectors of S viz. (0,0,1)^{T} can span whole [tex]\mathbb{R}^{3} [/tex].

b) It is not possible. Since if a set of vectors is linearly dependent then after adding linearly independent vectors it will also linearly dependent i.e. addition of a linearly independent vector does not effect on the set.


Related Questions

Five girls in a homeroom class of 20 students have blonde hair. If there are 120 students in the school, how many would you predict are blonde haired girls?

Answers

Step-by-step explanation: To find how many girls are blonde-haired, we'll have to subtract.

120 - 20 =

1. Subtract 0 by 0.

0 - 0 = 0

2. Subtract 2 by 2.

2 - 2 = 0

3. Since there isn't a number in the hundred's place, bring the 1 down.

Therefore, your answer is: 100. There are 100 blonde-haired girls.

In one classroom their is about 25% people that are blonde, so in 6 classes with 20 people each their would be 30 blonde haired girls.

p - 13 = 29
Can anyone help me with this

Answers

Answer:

42

Step-by-step explanation:

p - 13 = 29

Add 13 to both sides.

p - 13 + 13 = 29 + 13

p = 42

Answer:

p= 42

Step-by-step explanation:

29 plus 13 equals 42 which leaves p alone so p equals 42

A bag contains 4 green marbles, 3 red marbles, and 7

blue marbles. One marble is taken from the bag and put

back after checking its color. A second marble is then

taken out. What is the probability that the first is blue

and the second red?

Answers

Answer:

3/28

Step-by-step explanation:

There are 14 marbles in the bag.  So, the probability of choosing a blue marble is 7/14 or 1/2.  Since the first marble is replaced, the  bag still has 14 marbles in it.  Then the  probability of choosing a red marble is 3/14.  The probability of choosing the blue, then the red is 1/2 x 3/14 = 3/28

What percent of an hour is `24` minutes?

Answers

Answer:

24 minutes is equal to 24/60 x 100 = 40 percent of one hour

Step-by-step explanation:

40% is ur answer

Which of the following shows the solution and graph to the inequality
2x + 1 ≤ 15?

Answers

Answer:

x less than or equal to 7

Step-by-step explanation:

No graphs shown

Answer:

x<=7

Step-by-step explanation:

(x/2-3)/5=6 convert to english sentence​

Answers

when divided by 5, 3 subtracted from x divided by 2 equals to 6

(GIVING BRAINLYIST) 4 ÷ 1/2 YOU HAVE TO show your work on paper using fraction models!

Answers

Answer:

8

Step-by-step explanation:

so my school uses the method called kcf (keep change flip)

keep the 4

change the division sign to a multiplication sign

flip 1/2 to 2/1

4x2=8

Answer:

8 i first said two but used a caculater and found out it was 8

Step-by-step explanation:

PLEASE HELP ASAP I WILL TRY TO AWARD BRAINLYEST

Answers

Answer:

id say twice or one-third but im pretty stuiped so..

Step-by-step explanation:

What is 38 percent of 10 oranges

Answers

Answer:

The answer is 3.8

Explanation:

Move the decimal over once to the left.

Answer:

3.8 oranges.

Step-by-step explanation:

Step 1: Our output value is 10.

Step 2: We represent the unknown value with x.

Step 3: From step 1 above, 10=100%.

Step 4: Similarly, x=38%.

Step 5: This results in a pair of simple equations:

10=100%(1).

x=38%(2).

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both

equations have the same unit (%); we have

10/x= 100%/38%

Step 7: Again, the reciprocal of both sides gives

x/10 = 38/100

---> x=3.8$

Therefore, 38% of 10 is 3.8

This is 10 questions please answer. 1.Write the ratio as a fraction in the simplest form 15 girls to 6 boys. 2.Write The ratio as a fraction in simplest form 24 players: 3 teams.

3. Write The ratio as a fraction in simplest fraction form 48 worksheets: 12 students.

4. Tell whether the ratios form a proportion 4/7 the 4 is on top of the 7 24/35 the 24 is on top of the 35. 5. Tell whether the ratios form a proportion 11/12 11 top of the 12 33/36 33 on top of the 36. 6. 8/24 8 on top of 24 5/15 5 on top of the 15. 7.3/7 3 is on top of the 7 12/21 12 top of the 21 8. Tell whether the two rates form a proportion 25 cars in 5 days; 60 cars in 12 days.

9.14 books in 2 boxes; 20 books in 3 boxes.

10.On a monday you swim 12 laps in 30 minutes. On tuesday you swim 15 laps in 45 minutes are these rates porportional? Explain.

Answers

Answer and explanation:

1. 15 girls to 6 boys = 15:6

15/6= 5/2

2. 24 players to 3 teams = 24:3

24/3= 8/1=8

3. 48 worksheets to 12 students =48:12

48/12= 4/1

4. 4/7 and 24/35 are not proportional as they do not reduce to same ratio

5. 11/12 and 33/36 are proportional because they reduce to same same ratio(33/36=11/12)

6. 8/24 and 5/15 are proportional beacaue they reduce to same ratio(8/24=5/15=1/3)

7. 3/7 and 12/21 are not proportional because they do not reduce to same ratio(3/7≠12/21)

8. 25 cars in 5 days= 25/5= 5 cars each day. 60 cars in 12 days = 60/12=5 cars each day. Therefore they are proportional.

9. 14 books in 2 boxes= 7 books per box. 20 books in 3 boxes = 20/3= 6.667. Therefore they are not proportional.

10. 12 laps in 30 minutes =12/30=2/5

15 laps in 45 minutes =15/45=1/3. Therefore they are not proportional.

Heather went to the grocery store and only bought fruits and vegetables. She spent $3.42 on fruit and $4.74 on vegetables. Heather gave the clerk a $10 bill. Complete the equation below to find how much change she received.

Answers

Answer:

1.84$

Step-by-step explanation:

add 3.42 + 4.74 = 8.16 then 10 - 8.16 = 1.84

liters = 10,000 milliliters

How many liters do it equal?

Answers

Answer:

It will by 10

It equals 10 liters

mZWVA = 106°, m_AVU = 4x + 4,
and mZWVU = 21x + 8. Find x.

What is x?

Answers

9514 1404 393

Answer:

  x = 6

Step-by-step explanation:

If we assume that ray VA is between VW and VU, then we have ...

  ∠WVA + ∠AVU = ∠WVU

  106° +(4x +4)° = (21x +8)°

  102 = 17x . . . . . . . . . . . . . subtract 4x+8

  6 = x . . . . . . . . . . divide by 17

Could someone answer and explain. Will mark the brainliest

Answers

Answer: I think you’re right??

Step-by-step explanation:

The graph below shows the relationship between the amount of time in seconds to the distance traveled in feet by a cheetah

Answers

Answer:

where's the graph?

Step-by-step explanation:

hehehehe

(05.05 LC)
If you were to use the substitution method to solve the following system, choose the new
equation after the expression equivalent to x from the second equation is substituted into
the first equation. (5 points)
3x + 2y = -21
x-3y=4
3(3y + 4) + 2y = -21
O 31-3y + 4) + 2y = -21
3x + 2(3y + 4) = -21
3x + 21-3y + 4) = -21

Answers

Yes it is yep correct 1000% 10000000000000%

Pls help will give brainlest to first person who answer correct 50 points

Answers

Answer:

-25/3

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer/how I got this answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

Answer:

x = - 25/3

Step-by-step explanation:

10/3 = x/(-5/2)x = 10/3*(-5/2)x = - 25/3

Convert these mixed numbers into improper fractions.

2 2/3

1 4/7

Answers

Answer:

[tex]2\frac{2}{3}[/tex] = [tex]\frac{8}{3}[/tex]

[tex]1\frac{4}{7}[/tex] =  [tex]\frac{11}{7}[/tex]

Step-by-step explanation:

[tex]2\frac{2}{3}[/tex]

To convert a mixed number to an improper fraction all you need to do is......

Multiply the denominator of the fraction (3), by the whole number (the big number in front of the fraction) (2), and then you add the numerator....

Denominator times the whole number ( 3 * 2 = 6)

Now add the numerator with what you got ( 6 + 2 = 8)

Now the "8" will be the new numerator, and the denominator stays the same "3".

Improper fraction: [tex]\frac{8}{3}[/tex]

__________________________________________________________

[tex]1\frac{4}{7}[/tex]

We can do the same steps we did for the one above

Multiply the denominator (7) by the whole number (1), and then add the numerator (4)....

Denominator times whole number ( 7 * 1 = 7)

Add the numerator to the answer you got ( 7 + 4 = 11)

Now "11" will be the new numerator, and the denominator stays the same "7".

Improper fraction: [tex]\frac{11}{7}[/tex]

Hope this helped!

Have a supercalifragilisticexpialidocious day!

login.i-ready.com/student/dashboard/home
This box is inch long, 1 inch wide, and inch deep. What is the volume of the box?
Ź Inch
inch
Inch
33 inch
g inch
3
16
inch
12 inches

Answers

the volume of the box is 1 inch

Edward runs 30 miles in 5 days. Martha runs 28 miles in 4 days. Who runs more miles per day?

Answers

Edward because they completed more days and miles !!
Martha because 4 (days) divided by 28 (miles) is 7 (miles)

A. Function
B. Not a function

Answers

Answer:

a

Step-by-step explanation:

hope this helps

Help I will give Brainily in change!!!

Answers

Answer:

A

Step-by-step explanation:

The domain is the set of possible x values.

The given x-coordinates are -2, 1, 0, 3

Kindly solve this question for 15 points:
4 1/9 + 1 1/3 = ?

Answers

Answer:

5 4/9

Step-by-step explanation:

I did it myself

Evaluate the following expression when x = -2, y = 5, and t= 8.
[x]+3t-9y

Answers

Answer:

the answer is -23 let me if you have questions

simplify the following. 368+169

Answers

Answer:

537

Step-by-step explanation:

When i add the two i get a sum of 537.

Integrate [tex]e^{4x}\sqrt{1+e^{2x} } dx[/tex] please show work so i can learn

Answers

Answer:

the picture is attachedand sorry I can't explain you much about it

FIRST TO ANSWER GETS A BRAINLEIST

Answers

Answer:No

Step-by-step explanation:

They come out to different answers

Evaluate the polynomial when a. x = 0 and b. x= -1.
x² – 3x-7

Answers

Answer:

a. -7

b. -3

(i think)

Step-by-step explanation:

a.

x=0

0-0-7 = -7

b.

x=-1

1-3•(-3)-7

1+3-7

=-3

Which similarity statement and postulate or theorem correctly identifies the relationship?
B
D
12
E
86°
860

15
14
5
A
C
ОА
AABC - AFED by SSS Similarity Theorem
OB
AABC - ADEF by SAS Similarity Theorem
OC
AABC - AFED by AÁS Similarity Theorem.
OD
AABC - ADEF by AA Similarity Theorem

Answers

Answer:

It is side angle side

Step-by-step explanation:

The two sides of the triangle are around the angle

The similarity theorem that identifies the given relationship correctly would be:

B). AABC - ADEF by SAS Similarity Theorem

What is SAS Similarity?

The SAS similarity Theorem state that in the situation where the ratio shared by the sides of two triangles remains the same and one of their angles stays equal, both the triangles would be similar.

In the given two triangles,

ΔABC and ΔDEF

The ratio of the sides are:

[tex]\frac{BC}{AB} = \frac{EF}{DE}[/tex]

so,

[tex]\frac{5}{15} = \frac{4}{12} = \frac{1}{3}[/tex]

and,

∠B = ∠E = 86°

Since the ratios shared by the two sides are equal in both the given triangles and one angle is equal, the triangles are the same.

Thus,

ΔABC ~ ΔDEF

Learn more about "Theorem" here:

brainly.com/question/19258025

PLEASE ANSWER ASAP !!!!!!!!!!!!!!!!!!! WILL GET BRAINLEST IF CORRECT!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

b

Step-by-step explanation:

these are verticle angles so they will equal each other

3x=30

Answer:

B

Step-by-step explanation:

3x=30

Divide both sides by 3 and cancel the 3 on the left side.

x=10

Check by putting 10 for x

3(10)=30

30=30

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