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
8_murik_8 [283]
3 years ago
14

Prove that if the set of vectors {u1, u2, u3} is linearly dependent and u4 is any vector, then the set {u1, u2, u3, u4} is linea

rly dependent.
Mathematics
1 answer:
Lesechka [4]3 years ago
5 0

Answer with Step-by-step explanation:

We are given that the set of vectors{u_1,u_2,u_3} is lineraly dependent set .

We have to prove that the set {u_1,u_2,u_3,u_4} is linearly dependent .

Linearly dependent vectors : If the vectors u_1,u_2.u_3,u_4

are linearly  dependent therefore the linear combination

a_1u_1+a_2u_2+a_3u_3+a_4u_4=0

Then ,there exit a scalar which is not equal to zero .

Let a_1\neq0 then the vector u_1 will be zero and remaining  other vectors are not zero.

Proof:

When u_1,u_2,u_3 are linearly dependent vectors therefore, linear combination of vectors of given set

a_1u_1+a_2u_2+a_3u_3=0

By definition of linearly dependent vector

There exist a scalar which is not equal to zero.

Suppose a_1\neq 0 then  u_1=0

The linear combination of the set {u_1,u_2,u_3,u_4}

a_1u_1+a_2u_2+a_3u_3+a_4u_4=0

When a_1\neq0\; and\; u_1=0

Therefore,the set {u_1,u_2,u_3,u_4} is linearly dependent because it contain a vector which is zero.

Hence, proved .

You might be interested in
How do I solve this quadratic equations by factoring
Aleks [24]
If xy=0, assume that x and/or y=0

so we already gots factored
therfor
assume
3n-2=0 and 4n+1=0
solve

3n-2=0
3n=2
n=2/3

4n+1=0
4n=-1
n=-1/4


n=2/3 and/or -1/4
7 0
3 years ago
For the 2009 Major League Baseball and National Football League seasons, based on average ticket prices, Three baseball tickets
Marianna [84]

Answer:

I don't

Step-by-step explanation:

ena pa venum unaku enaku therla

5 0
2 years ago
51% of the tickets sold at a school carnival were early-admission tickets. If the school sold 100 tickets in all, how many early
saul85 [17]

Answer:

51 were the total number of the tickets sold at a school carnival were early-admission tickets.

Step-by-step explanation:

Total number of tickets sold by  = 100

Let x be the early-admission tickets sold by the school.

As 51% of the tickets sold at a school carnival were early-admission tickets.

so

x=\frac{51}{100}\times 100

  = 51

Therefore, 51 were the total number of the tickets sold at a school carnival were early-admission tickets.

5 0
3 years ago
one leg of a right triangle is 5 millimeters shorter than the longer leg and the hypotneuse is 5 millimeters longer than the lon
Makovka662 [10]
The answer, in short, is that the short leg equals 15 mm, the long leg equals 20 mm, and the hypotenuse equals 25mm. but if you'd like to see how I solved it, here are the steps.
-----------------------------
The Pythagorean theorem (also known as Pythagoras's Theorem) can be used to solve this. This theorem states that one leg or a right triangle squared plus the other side of that same triangle squared equals the hypotenuse of that triangle squared. To put it in equation form, L² + L² = H².

Let's call the longer leg B, the shorter leg A, and the hypotenuse H.
From the question, we know that A = B - 5, and H = B + 5. 

So if we put those values into an equation, we have (B - 5)² + B² = (B + 5)²

Now, to solve. Let's square the two terms in parentheses first:
(B² - 5B - 5B + 25) + B² = B² + 5B + 5B + 25

Now combine like terms:
2B² -10B + 25 = B² + 10B + 25

And now we simplify. Subtract 25 from each side:
2B² - 10B = B² + 10B

Subtract B² from each side:
B² - 10B = 10B

Add 10B to each side:
B² = 20B

And finally, divide each side by B:
B = 20

So that's the length of B. Now to find out A and H.
A = B - 5, so A = 15.
H = B + 5, so H = 25.

And your final answer is A = 15mm, B = 20mm, and H = 25mm
7 0
3 years ago
Toys R us is having a 38% off sale on all of their backpacks.If a backpack normally cost 22.00 how much will it be on sale
vovangra [49]

Answer:

$13.64

Step-by-step explanation:

The backpack is originally priced at $22. During the sale, the price would be 38% off which means you pay 62% of the original price. We can find this by multiplying by the percent 62 (converted into a decimal).


22(0.62)=13.64


The sale price at the sale is $13.64.

4 0
3 years ago
Other questions:
  • How do you solve the following equation: 5-(2x-3)=-8+2x
    13·1 answer
  • -3(-7) I need this asap pls help me
    12·2 answers
  • Gustion1
    7·1 answer
  • Question 1 (4 points)
    9·1 answer
  • How many (5in. by 5in. by 5in) cubes will occupy a classroom 9ft by 8ft by 7ft in dimension?
    14·1 answer
  • A bakery sells 25rolls for every 35 loaves of bread. At this rate, how many will be sold for every 7 rolls of bread?
    10·1 answer
  • What is (-8.1) + (-8.9) and please explain how
    5·2 answers
  • Simplify 5 − (−1).<br><br> a6<br> b−6<br> c4<br> d−4
    11·2 answers
  • Wendy thinks the perfect chocolate chip cookie has 353535 chocolate chips for every 555 ounces of dough. Cookie Club makes batch
    13·2 answers
  • Find the area of the triangle. Round your answer to the nearest tenth.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!