. prove that if v is a vector space having dimension n, then a system of vectors v1, v2, . . . , vn in v is linearly independent if and only if it spans v .

Answers

Answer 1

A system of vectors v1, v2, . . . , vn in a vector space v of dimension n is linearly independent if and only if it spans v.

Let's first assume that the system of vectors v1, v2, . . . , vn in v is linearly independent. This means that none of the vectors can be written as a linear combination of the others. Since there are n vectors and v has dimension n, it follows that the system is a basis for v. Therefore, every vector in v can be written as a unique linear combination of the vectors in the system, which means that the system spans v.

Conversely, let's assume that the system of vectors v1, v2, . . . , vn in v spans v. This means that every vector in v can be written as a linear combination of the vectors in the system. Suppose that the system is linearly dependent. This means that there exists at least one vector in the system that can be written as a linear combination of the others. Without loss of generality, let's assume that vn can be written as a linear combination of v1, v2, . . . , vn-1. Since v1, v2, . . . , vn-1 span v, it follows that vn can also be written as a linear combination of these vectors. This contradicts the assumption that vn cannot be written as a linear combination of the others. Therefore, the system must be linearly independent.

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Related Questions

can someone please explain this

Answers

Answer:

14 cm²

Step-by-step explanation:

1/2 (7•4)

1/2 (28)

14

Answer:14

Step-by-step explanation:

I believe it is asking you to multiply 4 and 7 getting 28, then divide that by 2 so 14

explain the arrangements of the atoms, I already have the first part done​

Answers

Step-by-step explanation:

The ongoing arrangement of metal atoms in a three-dimensional regular ordered pattern is known in chemistry as a lattice structure. A simple model of an atom is a central atomic nucleus with electrons arranged in shells at different distances from the nucleus.

A water bottle costs $9.45. Sales tax is 7%. What is the total cost?

Answers

Answer:

$10.11

Step-by-step explanation:

Before Tax Price: $9.45

Sale Tax: 7.00% or $0.66

After Tax Price: $10.11

Answer:

9.46

Step-by-step explanation:

divide 9.45 by .07 then add that to 9.45 and round

Consider the system of equations.

8x+2y=8

y= −4x+4

The system has blank solutions.
SELECT CHOICE
no,
infinitely many,
one.

Answers

then both equation r same after we re arrange it so no result

help me guysssssssssssssssss :D

Answers

Answer:

Slope=3

Step-by-step explanation:

m=y2-y1/x2-x1

m=19-10/6-3

m=3

Answer: The answer is C which is "m = 3"

Step-by-step explanation: To find the slope, the formula is change of y / change of x. The change of y in the graph is 9, and the change of x is 3. 9 divided by 3 is 3. Therefore, the option "m=3" is the correct answer.

If anyone can answer these questions that would help a lot. Besides 13 and 14

Answers

The answer to 12 is 10.

-2(-2-3)
10

2. Jules conducted a survey and asked 100
people how many years of education they have
and what their annual income is. She used the
results to make a scatter plot.

What type of assoastion should she expect to see in the scatter plot

Answers

"Positive association" would be the answer.

A store has apples on sale for $21.00 for 6 pounds. If an apple is approximately 5 ounces, how many apples can you buy for $126.00? Complete the explanation.

Answers

Answer:

115 apples

Step-by-step explanation:

6 pounds of apple = $21.00

Cost per pound :

$21.00 / 6 = $3.5 per Pound

1 pound = 16 ounces

16 ounces cost $3.5

1 ounce = $3.5 / 16 = $0.21875

5 ounces will cost :

5 * 0.21875 = $1.09375

Number of 5 ounce apple that can be purchased with $126

$126 / $1.09375

= 115.2

Approximately 115 apples

are the rates equivalent?

Answers

Answer:

No

Step-by-step explanation:

0.3/4= 0.075

0.9/15= 0.016

They aren't equal.

Answer:

no they are not

Step-by-step explanation:

cause I said

Need help with this problem

Answers

m∈(-∞,-4)∪(4,+∞)

Step-by-step explanation: Photo Math App

Can anyone help me please
I’ll mark brainliest.

Answers

Answer:

1. his account will be 120

2. 6 weeks

3. Yes, Lala will get 120 in 4 weeks while Andra will get 100

If you wanted to know Andra equation will be y=20x+20

Step-by-step explanation:

Hope this helped

Find a positive angle that is less than 360° that is coterminal with a -80°
angle
*
260°
440°
-440°
None of the above

Answers

none of the above
hope this helps :)
None of the above the answer would be 205
May God bless you and your family

epic math question that i cant solve

Answers

the area of the shaded region can be found by subtracting the area of the inside rectangle from the outside rectangle

area of outside: 6 X 10y —> 60y
area of inside: 3 X 5x —> 15x

so the area of the shaded region is 60y-15x

the GCF is 15, so the factored form is: 15(4y-x)

hallar 4 números naturales pares consecutivos cuya suma sea igual a 44​

Answers

Answer:

11+11+11+11=44

Do I have to use different numbers?

10+14+12+8=44

1. Use a trigonometric ratio to determine the value of x for each the
triangle. Round your answer to the nearest hundredth. *
8 mm
Х
26°

Answers

Read the top and you have your answer
The trigonmetric ratio is the answer... And if not then try brainlys quick answers

What are three other names for range. ( This is for algebra)

Answers

Answer: area.
dimension.
length.
scope.

The measures of the angles of a triangle are shown in the figure below.Solve for X.

Answers

Answer:

x=3

Step-by-step explanation:

51 degrees + (7x+18) degrees = 90 degrees

7x+18=90-51

7x+18=39

7x+18-18=39-18

7x=21

7x/7=21/7

x=3

Which expression is represented by the model below?

2 bars are shown next to each other and each bar is labeled

A.
8
×
2
3
B.
3
×
2
8
C.
8
×
3
2
D.
2
×
3
8

Answers

Answer

its d

Step-by-step explanation:

The expression that is represented by the model below is -

y = 2 x 3/8.

What is expression in mathematics?

An expression in mathematics is a combination of terms both constants and variables.

Given are two labelled bars shown next to each other and each bar.

3 of the 8 bars are colored. Using fraction, we can represent it as -

{f} = 3/8

There are two such bars, so we can write -

y = 2{f}

y = 2 x 3/8

Therefore, the expression that is represented by the model below is -

y = 2 x 3/8.

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Is -3x+5=-3x+8 infinate many solutions

Answers

Maybe




Know knows, calculate it

Two lines A and B are parallel if both lines are rotated 90° in the same direction and then translated to the right by the same number of units which statement about the lines resulting from these transformations is true

Answers

Answer:

A' and B' will be parallel. (See Explanation)

Step-by-step explanation:

Given

Parallel lines: A and B

Rotation: 90° same direction

Translation: Right (same units)

Required

Describe the result of the transformation

No options were given. So, I will answer on general terms.

From the question, we can see that, the same transformation that was performed on line A was also done on line B.

This means that both lines will maintain the initial relationship between them.

Initially, A and B are parallel.

After the transformation, A' and B' will be parallel.

Answer:They will be the same line

Step-by-step explanation:I did this on my test it’s correct


Please help me -5x-3y=16 y=x

Answers

Answer:

the answer is x=2 and y=2

Step-by-step explanation:

-3y=16+5x

-y=(16+5x)3

Use the following table to find the Rate of Change.

Answers

Answer:

x=1 and y= 6

Step-by-step explanation:

and for y its a positive cause their both negitives

Please answer for kind of a lot of points :D

Answers

a)3.5d +5 + 2.5d + 3

= 6d +8

Answer:

(5.5d + 8) miles27.5 miles

Step-by-step explanation:

Lyndsay ⇒ 3d + 5Seth       ⇒ 2.5d + 3

a) Together they run:

3d + 5 + 2.5d + 3 = (5.5d + 8) miles

b) They run 5 days Monday through Friday last week:

5.5*5 = 27.5 miles

15•(13 - 7) ÷ (8 - 5) Simplify

Answers

Answer:

30

Step-by-step explanation:

15•(13-7)÷(8-5)

15•(6)÷(3)

90÷3

30

Answer:

30

Step-by-step explanation:

15 x 6 / 3 =

90 / 3 =

30

Hope that helps!

2x-6y=12 and -5x+15y=-30 elimination

Answers

Answer:

unsolvable because the second equation is just -2.5 times the first equation.

Step-by-step explanation:

2x-6y=12    then   2x=12+6y     x=6+3y

-5x+15y=-30

substitute x

-5(6+3y)+15y=-30

-30-15y+15y=-30

y=y

PLEASE HELP ME!! I will give brainliest

Answers

Answer:

D

Step-by-step explanation:

It is on the positive side of the graph and the point is on 3,1

I need help with this

Answers

9514 1404 393

Answer:

perimeter: 20 unitsarea: 27.5 square units

Step-by-step explanation:

We must assume the pentagon is regular. Its 5 sides are all the same length as AB, which is 4 units. So, the perimeter is ...

  P = 5s = 5(4) = 20 . . . units

__

The area is given by the formula ...

  A = (1/2)Pa

where P is the perimeter and a is the apothem--the distance from the center to one side.

The center coordinates are (3, 4.75), so the center is 2.75 units from side AB at y=2. Then the area is ...

  A = (1/2)(20)(2.75) = 27.5 . . . square units

imao help me with zearn

Answers

Answer:

4

Step-by-step explanation:

if there are 8 ounces for 2 then there are 4 ounces for 1.

Answer:

with what?

Step-by-step explanation:

Please help ASAPPPPPO

Answers

Answer:

x=all real numbers

y=all real numbers

Step-by-step explanation:

x=-5y-1

-3(-5y-1)-15y=3

15y+3-15y=3

3=3

therefore the answer is all real numbers

What type of decimal is 0.275

A. Repeating Decimal
B. Terminating Decimal
C. Non-Terminating Decimal
D Complex Decimal

Answers

D. Complex Decimal.

Answer:

Complex Decimal.

it is the correct answer.

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