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
2 option question NEED ANSWER NOW PLZ
castortr0y [4]
Do you have a text book?

8 0
3 years ago
The home for sale is listed at $150,000.00. They have $30,000.00 for a down payment and are qualified for a fixed rate 30-year m
klio [65]

Answer:

Estimate: $900.00

Step-by-step explanation:

This cannot be A, B, or C, as it won't make sense with the increase of 75$ each 4 years, with 30K down payment,

3 0
2 years ago
Read 2 more answers
Stacey and Michele both babysit in the evening.staceys hours rate is $10 for one child plus $2per additional child Michael hourl
lara31 [8.8K]
They have two children...
8 + 3c = 10 + 2c
c = 2
7 0
3 years ago
Read 2 more answers
Find the gcf of 40 and 60 listing factors for each number in order from least to greatest. report each list of factors, and then
Olegator [25]
Factors of 40: 1,2,4,5,8,10,20,40
Factors of 60: 1,2,3,4,5,6,10,12,15,20,30,60
Greatest common factor of both is 20.
8 0
3 years ago
A restaurant has a total of 30 tables which are of two
ki77a [65]

Answer:

Total number of tables of first type       = 23.

Total number of tables of second type = 7

Step-by-step explanation:

It is given that there are 30 tables in total and there are two types of tables.

Let's call the two seat tables, the first type as x and the second type as y.

∴                                             x + y = 30                        ......(1)

Also a total number of 81 people are seated. Therefore, 2x number of people would be seated on the the first type and 5y on the second type. Hence the equation becomes:

                                            2x + 5y = 81                        .....(2)

To solve (1) & (2) Multiply (1) by 2 and subtract, we get:

                                                      y = 7

Substituting y = 7 in (1), we get x = 23.

∴ The number of tables of first kind         = 23

  The number of tables of second kind   = 7

4 0
3 years ago
Other questions:
  • Which set of line segments could create a right triangle? 5, 6, 11 5, 9, 10 5, 13, 18 5, 12, 13
    15·2 answers
  • two owls leave the same tree at 9:00 p.m. One owl flies west at 7 miles per hour and the other flies east at 13 miles per hour.
    8·2 answers
  • A washer and a dryer cost $942 combined. The washer costs $42 more than the dryer. What is the cost of the dryer?
    8·2 answers
  • In a school with only sixth and seventh-grade students, 2/5 of the 200 students are seventh graders
    13·2 answers
  • George wishes to increase the percent of acid in 50ml of a 15% acid solution in water to 25% acid, how much pure acid must you a
    7·2 answers
  • What is the value of 8C5? A. 40 B. 56 C. 960 D. 6720
    10·2 answers
  • Explorers on a planet with a thin atmosphere want to measure the acceleration of gravity at its surface. So they use a spring gu
    11·1 answer
  • .......................hi I'm board
    13·2 answers
  • What is the perimeter of the trapezoid? In unit
    9·1 answer
  • 3)
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!