let u and v be subspace of a vector space w . show that if w = u ⊕v then u ∩v = {0}.

If W = U ⊕ V, then U ∩ V = {0} which can be proved by proving {0} is an element of U ∩ V and there are no other elements in U ∩ V besides {0} for the vector space.

To show that if W = U ⊕ V, then U ∩ V = {0}, we need to prove two things:

1. {0} is an element of U ∩ V.
2. There are no other elements in U ∩ V besides {0}.

Step 1: Show that {0} is an element of U ∩ V.

Since U and V are subspaces of the vector space W, they both must contain the zero vector (0) as per the definition of a subspace. Therefore, the zero vector is in both U and V, which implies that 0 is an element of U ∩ V.

Step 2: Show that there are no other elements in U ∩ V besides {0}.

Suppose there is a nonzero vector x that belongs to U ∩ V. This means x is in both U and V. Since W = U ⊕ V, any vector in W can be uniquely written as the sum of a vector from U and a vector from V. Thus, x can be written as:

x = u + v

where u is a vector from U and v is a vector from V. However, x is also in both U and V, so we can rewrite the equation as:

x = x + 0

Since the sum of vectors from U and V is unique, we must have u = x and v = 0. But this contradicts our initial assumption that x is a nonzero vector, as x ∈ V and we assumed x ≠ 0. Therefore, there can be no other elements in U ∩ V besides {0}.

In conclusion, if W = U ⊕ V, then U ∩ V = {0}.

Learn more about vector space here:

https://brainly.com/question/13058822

#SPJ11

Can someone please help me ASAP

1/4 y + 9=1/2 A -34 b 2 c 9 d 38

Need help ASAP 25 points

Write an solve the inequality. A gym charges a one time sign-up fee of $10.25 and then $5 each time you go. A student can pay up to $135.25. How many times can the student go to the gym?

Solve for x and y.
8
5
Х
15
У
12

Which expression represents the factor form of the equation above ?

George wants to buy a new television that is on sale for 1/4 off the regular price of $599.96. The sales tax is 7%. What is the final price of the television including tax? ​

find the value of -
[tex]( {x}^{2} - x)[/tex]
where, x = 5
​

A bag has some purple marbles and
some green marbles in it. This can be
modeled with the following equation.
T = p + g.
Solve the equation for the number of
purple marbles, p.
Enter the variable that belongs in the green box.
p = [?] - [ ]

need to know the middle part

what is the ratio then what is the value of the ration?

the length and breadth of a hall are 20m and 15m respectively. find the area of 4 Walls of the hall if the height of the hall is 10 m​

if sin theta = cos theta,theta is an acute angle then tan theta=?
please answer within one hour
I will mark u brainliest​

Slope of 4,-9 and 8,-3

Find the product of 2x4(3x2 + 4x + 1).
6X6 + 8x5 + 2x4
6x3 + 3x4+1
5X6 + 6x5 + 3x4
5x8 + 6x4 + 1​

Help please and tysm

6 x (5 + 4) - 3 - (2+1)

A 18
B) 30
C) 48
D) 54

if the slop of the straight line passing through the two points A (4, k) , B (3, 2) is 5, find the value of K

Find the square root. 1/16​

Find the point-slope equation for the line that passes through the points (-6, 24) and (5, -31). Use the first point in your equation. y - [?] = [ ](x-[ ])​

On a loan of $4,500 for 2 1/2 years at 4% per year, how much do you wind up paying to pay off the loan?

Determine if the triangles are congruent by HL, SAS, SSS, AAS, or
ASA

Somebody help please!!!

A rectangle has a length of 2y inches and a width of y - 4 inches. If the perimeter of the rectangle is 22 inches, what is y? What is the length? What is the width?

jake has a recipe that uses 4 cups of flour. He has a bag with 48 cups of flour. He wants to know how many recipes he can make using the bag of
flour. He finds the answer using this number sentence:
48 4=
Which number sentence shows another way to solve this problem?
A x 4 = 48
B. 48 x = 4
C 0 : 4 = 48
D. 4: 48 = 0

What's the circumference of a circle with a radius of 5 inches

ayo!! listen to me this is an easy question :)

Apples are on sale at the local fruit stand at 4 lbs. for $2.60. Which equation can be used to find the cost, c, of n pounds of apples?
c = 4
c = .65n
c = 2.60n
c = 8n

PLS SHOW HOW YOU SOLVED THE PROBLEM
15. The perimeter of an isosceles triangle is 34 inches. When you add the base of the
triangle to one of the equal sides the sum is 18. What is the length of the base of the
triangle?
a)
2 inches
go to card 3
b) 14 inches
go to card 6
c) 9 inches
go to card 9
d) 16 inches
go to card 11
e) 4 inches
go to card 13

3x-4y=-14 6x+3y=27 don’t understand how to solve

A sailboat with a sick passenger abroad is following a parabolic path given by the equation = − 2 +2 + 8.
The boat’s captain sent out a distress signal. A speedboat is trying to catch the sailboat to provide medical aid and is on a path given by the linear equation y=- x+8. Besides the y-intercept (starting location) where do the paths of the two boats cross (for each graph you must plot at least 3 points each and give answer in coordinate pair notation)?

A savings account earns 7% interest each year, compounded quarterly (4 times a year). If a person invests $300 and makes no further deposits or withdrawals, what is the balance in the account after 5 years​

Mr. Mika paid a total of $150 to rent a room at a hotel for two nights. The table shows information about four other
guests who rented rooms at the hotel.
Hotel Bills
Number of Nights
Room Was Rented
Total Amount
Paid
Guest
1
6
$450
II
3
$225
III
8
$600
IV
5
$360
Which guest did NOT pay the same nightly rate that Mr. Mika did?