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
Hoochie [10]
3 years ago
8

The statement is either true in all cases or false. If false, construct a specific example to show that the statement is not alw

ays true. If v_1, ......, v_4 are in R^4 and v_3 = 2v_1 + v_2, then {v_1, v_2, v_3, v_4} is linearly dependent. Choose the correct choice below and, if necessary, fill in the answer boxes to complete your choice. a. True Because v_3 = 2v_1 +v_2, v_4 must be the zero vector. Thus, the set of vectors is linearly dependent. b. True. The vector v_3 is a linear combination of v_1 and v_2, so at least one of the vectors in the set is a linear combination of the others and set is linearly dependent. c. True. If c_1 =2, c_2 = 1, c_3 = 1, and c_4 = 0, then c_1v_1 + middot middot middot + c_4v_4 =0. The set of vectors is linearly dependent. d. False. If v_1 =, v_2 =, v_3 =, and v_4 = [1 2 1 2], then v_3 = 2v_1 + v_2 and {v_1, v_2, v_3, v_4} is linearly independent.
Mathematics
1 answer:
natali 33 [55]3 years ago
4 0

Answer: The correct option is (B).

True. The vector V₃ is a linear combination of V₁ and V₂, so at least one of the vectors in the set is a linear combination of the others and set is linearly dependent.  

Step-by-step explanation:  

Given that;

If V₁ ....... V₄ are in R⁴ and V₃ = 2V₁ + V₂ then {V₁, V₂, V₃, V₄} is linearly dependent.  

Lets {V₁, V₂, V₃, V₄}  are linearly dependent

Then there exist a scalars C₁, C₂, C₃, C₄

So that C₁V₁ + C₂V₂ + C₃V₃ + C₄V₄ = 0

where at least one of the Ci ≠ 0.  

Take C₃ ≠  0 then we have V₃ = (C₁V₁ + C₂V₂ + C₄V₄) / C₃

V₃ is a linear combination of V₁, V₂ and V₄}

that is

Given V₃ = 2V₁ + V₂

⇒ 2V₁ + V₂ - V₃ = 0

⇒ 2V₁ + V₂ + V₃ + 0V₃ = 0

Here, C₁ = 1, C₂ = 1,  C₃ = -1 and C₄ = 0

So that {V₁, V₂, V₃, V₄} is linearly dependent.

therefore option B id the right answer.

- True. The vector V₃ is a linear combination of V₁ and V₂, so at least one of the vectors in the set is a linear combination of the others and set is linearly dependent.  

You might be interested in
What is the discriminant of 9x2 + 2 = 10x?<br> –356 <br> –172 <br> 28<br> 72
Airida [17]

Answer:

<h2><em>C. 28</em></h2>

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
PLEASE HALP ME! ( WILL MARK BRAINLIEST! Thank you! ;)
Semmy [17]

Answer: 1/20

Step-by-step explanation:

Decimal Fraction Percentage

0.05 1/20          5%

5 0
3 years ago
Read 2 more answers
Square root of 3<br> Square root of 36<br> Square root of 9<br> Which number is irrational?
coldgirl [10]

Answer:

Square root of 3

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
35 and 50 (make a chart, list all factors, and make factor tree)
quester [9]

Answer:

35          50

1             2

5            5

7            10

35         25

             50

Factor Trees are in the images!

5 0
3 years ago
7x2 + 4x - x2 whats the answer?!?
zepelin [54]

Answer:

14 + 2x I think

Step-by-step explanation:

Wait for more responses if needed

3 0
3 years ago
Read 2 more answers
Other questions:
  • In a certain year, the U.S. Senate was made up of 53 Democrats, 45 Republicans, and 2 Independents who caucus with the Democrats
    13·1 answer
  • Show that the sum of two concave functions is concave. Is the product of two concave functions also concave?
    6·1 answer
  • A triangle with three acute angles and no congruent sides
    6·1 answer
  • Assume each variable has a different value. Which relations below are functions?
    15·1 answer
  • Helppppp❤️ Please please
    7·1 answer
  • Show how you could set up and find the exact value of cos(5π/4) in two different ways.
    8·1 answer
  • Find the range of the following data. Scores:81,79,80,88,72,96,86,73,79,88
    9·1 answer
  • HELP PLEASE!! Math question— Please explain,,,
    9·1 answer
  • HELPPPPPPPPPPPPPPPPPPPPPPPP
    7·2 answers
  • Jamie needs 1/5 meter of ribbon to decorate the border of a photo frame. Enter the number of photo frames that can be decorated
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!