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
aleksklad [387]
3 years ago
12

Consider the following set of vectors. v1 = 0 0 0 1 , v2 = 0 0 3 1 , v3 = 0 4 3 1 , v4 = 8 4 3 1 Let v1, v2, v3, and v4 be (colu

mn) vectors in ℝ4 and let A be the 4 ✕ 4 matrix v1 v2 v3 v4 with these vectors as its columns. Then v1, v2, v3, and v4 are linearly dependent if and only if the homogeneous linear system with augmented matrix [A|0] has a nontrivial solution. Consider the following equation. c1 0 0 0 1 + c2 0 0 3 1 + c3 0 4 3 1 + c4 8 4 3 1 = 0 0 0 0 Solve for c1, c2, c3, and c4. If a nontrivial solution exists, state it or state the general solution in terms of the parameter t. (If only the trivial solution exists, enter the trivial solution {c1, c2, c3, c4} = {0, 0, 0, 0}.)
Mathematics
1 answer:
Alona [7]3 years ago
4 0

Answer:

We have the equation

c_1\left[\begin{array}{c}0\\0\\0\\1\end{array}\right] +c_2\left[\begin{array}{c}0\\0\\3\\1\end{array}\right] +c_3\left[\begin{array}{c}0\\4\\3\\1\end{array}\right] +c_4\left[\begin{array}{c}8\\4\\3\\1\end{array}\right] =\left[\begin{array}{c}0\\0\\0\\0\end{array}\right]

Then, the augmented matrix of the system is

\left[\begin{array}{cccc}0&0&0&8\\0&0&4&4\\0&3&3&3\\1&1&1&1\end{array}\right]

We exchange rows 1 and 4 and rows 2 and 3 and obtain the matrix:

\left[\begin{array}{cccc}1&1&1&1\\0&3&3&3\\0&0&4&4\\0&0&0&8\end{array}\right]

This matrix is in echelon form. Then, now we apply backward substitution:

1.

8c_4=0\\c_4=0

2.

4c_3+4c_4=0\\4c_3+4*0=0\\c_3=0

3.

3c_2+3c_3+3c_4=0\\3c_2+3*0+3*0=0\\c_2=0

4.

c_1+c_2+c_3+c_4=0\\c_1+0+0+0=0\\c_1=0

Then the system has unique solution that is (c_1,c_2c_3,c_4)=(0,0,0,0) and this imply that the vectors v_1,v_2,v_3,v_4 are linear independent.

You might be interested in
1.1 solve for x, where 0°< x 90°. write your answer to one decimal place. 1.1.1 tanx=sin38° 1.1.2cosec( x+10°)=1.345​
snow_lady [41]

The value of x in tan(x)=sin38° is 31.6 and the value of x in cosec(x+10°)=1.345​ is 38.0

<h3>How to solve the trigonometry ratios?</h3>

The equations are given as:

tan(x)=sin38°

cosec( x+10°)=1.345​

In tan(x)=sin38°, we have:

tan(x)=0.6157

Take the arc tan of both sides

x = 31.6

Also, we have:

cosec(x+10°)=1.345​

Take the inverse of both sides

sin(x+10°) = 0.7434

Take the arc sin of both sides

x+10 = 48.0

Subtract 10 from both sides

x = 38.0

Hence, the value of x in tan(x)=sin38° is 31.6 and the value of x in cosec(x+10°)=1.345​ is 38.0

Read more about trigonometry ratios at:

brainly.com/question/11967894

#SPJ1

5 0
2 years ago
Tapiwa takes 5% more leaves than adam raked. together they raked 697 liters of leaves
Nina [5.8K]
----------------------------------
Define their percentage:
----------------------------------
Adam = 100%
Tapiwa = 100 + 5 = 105%

----------------------------------
Find their total percentage:
----------------------------------
100 + 105 = 205

----------------------------------
Find 1%
----------------------------------
205% = 697 liters
1% = 3.4 liters

----------------------------------
Find 100% (Adam):
----------------------------------
100% = 3.4 x 100
100% = 340 liters

----------------------------------
Find 105% (Tapiwa):
----------------------------------
105% = 3.4 x 105 
105% = 357 liters

--------------------------------------------------------------------
Answer: Tapiwa =  357 liters and Adam = 340 liters.
--------------------------------------------------------------------

8 0
3 years ago
Select all that apply
katovenus [111]
The range is Y>2. :) 
5 0
3 years ago
I dont know how to solve this one ​
Olenka [21]

Answer:

The answer is the second option or B, you have to divide the top number by the bottom number to get a unit rate.

5 0
3 years ago
Read 2 more answers
I don't get this can someone help me with this
kati45 [8]
P= $48c + $17.76 hope this helps

8 0
3 years ago
Other questions:
  • 3m2+7=55 answer please
    14·1 answer
  • ASAP!!!!
    11·1 answer
  • How many lines of symmetry does this figure have?
    8·2 answers
  • 3x + 1 &gt; 7<br> Solve ^<br> Help please it's for a test ​
    5·2 answers
  • W=2, p=3 ........ 5p-2w
    15·1 answer
  • Please help me I need to turn in tomorrow
    13·2 answers
  • The general solution of sinx + cosx =√2 is..??​
    5·2 answers
  • 3^9 times 3^7 in exponential form
    7·2 answers
  • To win a​ lottery, 7 numbers are drawn at random from a pool of 21 numbers. Numbers cannot repeat. If a person has one​ ticket,
    15·2 answers
  • NEED HELP IMMEDIATELY PLEASE HELP
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!