1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Vanyuwa [196]
2 years ago
9

Could a set of three vectors in ℝ^4 span all ℝ^4? Explain. What about n vectors in ℝ^m when n is less than m?

Mathematics
1 answer:
Elena-2011 [213]2 years ago
8 0

Answer:

Check the ecplanation

Step-by-step explanation:

A set of three vectors in R^{4} represents a matrix of 3 column vectors, and each vector containing 4 entries (that is, a matrix of 4 rows, and 3 columns).

Let A be that 4x 3 matrix. The columns of A span R^{m}. if and only if A has a pivot position in each row. So, there are at most 3 pivot positions in the matrix A, but the number of rows is 4, therefore, there exist at least one row not having a pivot position. If A does not have a pivot position in at least one row, then the columns of A do not span R^{4}. It implies that the set of 3 vectors of A does not span all of R^{4}.

In general, the set of n vectors in R^{m} represents a matrix of in rows, and n columns (an in x matrix). So, there are at most n pivot positions in the matrix A, but n is less than the number of rows. In therefore, there exist at least one row that does not contain a pivot position.

And, hence the set of n vectors of A does not span all of R^{m}. for n < m

You might be interested in
A school band gives a year-end concert. It is held in a 400-seat auditorium. Each concert ticket sells for $10, and 85% of the t
bazaltina [42]

Answer: $3,400

Step-by-step explanation:

There are 400 seats in the auditorium which means that there are 400 tickets to be sold.

85% of these tickets are sold. The number of tickets sold is:

= 85% * 400

= 340 tickets were sold.

Each ticket sells for a total of $10.

The amount of money made from ticket sales is therefore:

= No. of tickets sold * price of ticket

= 340 * 10

= $3,400

6 0
3 years ago
A marketing representative wants to estimate the proportion of people in a state who like the new design on the packaging of a c
Effectus [21]

Answer:

The correct option is;

(B) Yes, because sampling distributions of population proportions are modeled with a normal model.

Step-by-step explanation:

Here we have the condition for normality being that where we have a population with a given mean and standard deviation, while a sufficiently large sample is drawn from the population while being replaced, the distribution of the sample mean p will be distributed normally according to central limit theorem.

8 0
2 years ago
The bottom of a box is to be a rectangle with a perimeter of 36 CM. The Box must be 4 cm High. What is the maximum volume?
Amanda [17]

The maximum volume would be when the bottom of the box is a square.

The perimeter of the bottom is 36, so the side of the square would be 36/4 = 9 cm.

Then to find volume multiply the length by the width by the height:

Volume = 9 x 9 x 4 = 324 cm^3

The answer would be a.

8 0
3 years ago
Read 2 more answers
a rectangle has sides that are 23 m 19 m and 19 m what is a rectangles lengthA. 19 mB. 23 mC. 84 mD. 46 mthis is what it said Th
sdas [7]

Given Data:

The sides of the rectangle are 23 m, 23 m ,19 m and 19 m.

The length of the rectangle is 23 m.

Thus, option (B) is the correct option.

4 0
1 year ago
PLS HELP ME I’VE ASKED THIS TWICE AND NOBODY HAD ANSWER THIS IS REALLY EASY TO DO
laiz [17]

Answer:

Step-by-step explanation:

All the angles within a triangle equals to 180, and that square thing at a corner of the triangle means that the angle is 90 degrees, so:

20+6x+16+90=180

add stuff

6x+126=180

subtract 126 from both sides

6x=54

divide 6 from both sides

x=9

6 0
3 years ago
Other questions:
  • Write an equation of the line in point slop form that passes through the two given points
    5·1 answer
  • PLZ HURRY IT'S URGENT!!
    14·2 answers
  • Duffy was analyzing the trajectory made after throwing a football. his coach was able to measure that his throw reached a maximu
    11·1 answer
  • please answer the questions circled aka: Lillie’s grandmother is making potato salad for a family reunion. She uses three potato
    11·2 answers
  • I need help with these questions​
    9·2 answers
  • Julio has 5 more dollars than Dan. Altogether, Julio and Dan have $19. Write and solve an equation to represent the situation. H
    14·1 answer
  • Find the sum x^2-2x-15 and 2x^2+5x-2
    10·1 answer
  • HELPP PLS AND THANK YOU
    11·1 answer
  • the length of a rectangular garden is 4 feet longer than the width. if the perimeter is 192 feet, what is the area is the garden
    14·1 answer
  • Brainliest points whatever you want please
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!