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
Mekhanik [1.2K]
3 years ago
11

Show that there do not exist scalar c1 c2 and c3 c1(-2,9,6)+c2(-3,2,1)+c3(1,7,5)= (0,5,4)​

Mathematics
1 answer:
fredd [130]3 years ago
5 0

This is the same as showing the following system of equations doesn't have a solution:

\begin{cases}-2c_1-3c_2+c_3 = 0 \\ 9c_1 + 2c_2 + 7c_3 = 5 \\ 6c_1 + c_2 + 5c_3 = 4\end{cases}

or in matrix form,

\begin{bmatrix}-2&9&6\\-3&2&1\\1&7&5\end{bmatrix}\begin{bmatrix}c_1\\c_2\\c_3\end{bmatrix} = \begin{bmatrix}0\\5\\4\end{bmatrix}

The quickest way to check if there is a solution is to check whether the coefficient matrix is invertible. If its determinant is 0, then it is not invertible.

And the quickest way to show that the determinant is 0 is by observing that the third row is a linear combination of the first two rows:

(-2, 9, 6) - (-3, 2, 1) = (-2 + 3, 9 - 2, 6 - 1) = (1, 7, 5)

So there are indeed no such scalars <em>c₁</em>, <em>c₂</em>, and <em>c₃</em>.

You might be interested in
Help please and thank you
lara [203]
Cannot be determined.
Area or perimeter should be provided to calculate the lenght but its not.
8 0
3 years ago
Can somebody help mee plzzzzzzzz
hammer [34]

Answer:

lines a and b are parallel. The slopes are -1/3

None of the lines are perpendicular to each other.

Step-by-step explanation:

To figure out if any of the lines are parallel or perpendicular to each other, you have to find the slopes of each line. To find the slope look at the graph find the rise over run for all of the lines:

line a: This line goes down one every time it goes over 3, which can be represented by -1/3

line b: This lines goes down one every time it goes over 3, which can also be written as -1/3

line c: This line goes up 5 every time it goes over 2, which makes the slope 5/2

When two lines are parallel, they have the same slope. Line a and line b have the same slope, so they are parallel.

When two lines are perpendicular, their slopes are negative reciprocals of each other. Since none of the slopes are a negative reciprocal of another slope, we have no perpendicular lines.

Hope this helps :)

7 0
3 years ago
A box has dimensions of 17 inches long 1.3 feet wide and 8 inches high what is the volume of the box the formula of the volumes
nataly862011 [7]
The box is about 2121.6 inches cubed
8 0
3 years ago
What are the roots of the polynomial equation XP-7x= 6x-12? Use a graphing calculator and a system of equations.
Julli [10]

Answer: option B

Step-by-step explanation:

-4, 1, 3

6 0
3 years ago
What is the answers for 3 through 6?
jasenka [17]
3) 2 to 3
4) 4 to 5
5) 5 to 6
6) 5 to 7

ur welcome kid






5 0
3 years ago
Read 2 more answers
Other questions:
  • A building is 200ft long and 140 ft wide a 1/500 model is built of the building how long and how wide is the model?
    10·1 answer
  • 4 times the sum of a number and 5 is 1 less than the same number
    8·1 answer
  • Find the slope of the line. <br><br> A. 1/7<br><br> B. - 1/7<br><br> C -7<br><br> D. 7
    8·1 answer
  • 02
    8·1 answer
  • Need help really bad
    8·1 answer
  • Round the number 502.6439 to the underlined place. The underlined number is 3
    12·1 answer
  • 9 less than a number is -1.​
    14·2 answers
  • Can anyone do this thanks
    15·1 answer
  • Find the explicit of 3xy+x=y-6
    8·1 answer
  • Which sets of angles add to equal 180°?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!