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
STatiana [176]
3 years ago
7

For waht values of x do the vectors -1,0,-1), (2,1,2), (1,1, x) form a basis for R3?

Mathematics
1 answer:
DaniilM [7]3 years ago
4 0
<h2>Answer:</h2>

The values of x for which the given vectors are basis for R³ is:

                        x\neq 1

<h2>Step-by-step explanation:</h2>

We know that for a set of vectors are linearly independent if the matrix formed by these set of vectors is non-singular i.e. the determinant of the matrix formed by these vectors is non-zero.

We are given three vectors as:

(-1,0,-1), (2,1,2), (1,1, x)

The matrix formed by these vectors is:

\left[\begin{array}{ccc}-1&2&1\\0&1&1\\-1&2&x\end{array}\right]

Now, the determinant of this matrix is:

\begin{vmatrix}-1 &2 & 1\\ 0& 1 & 1\\ -1 & 2 & x\end{vmatrix}=-1(x-2)-2(1)+1\\\\\\\begin{vmatrix}-1 &2 & 1\\ 0& 1 & 1\\ -1 & 2 & x\end{vmatrix}=-x+2-2+1\\\\\\\begin{vmatrix}-1 &2 & 1\\ 0& 1 & 1\\ -1 & 2 & x\end{vmatrix}=-x+1

Hence,

-x+1\neq 0\\\\\\i.e.\\\\\\x\neq 1

You might be interested in
A store purchased a DVD for $12.00 and sold it to a customer for 50% more than the purchase price. The customer was charged a 7%
olga55 [171]

Answer:

$19.26 or $19.

Step-by-step explanation:

Sold DVD for 50% more of the purchase price of $12, so:

12 + 50/100 * (12) = 12 + 6 = 18.

The customer will pay 7% tax on $18.

18 * (1.07) = $19.26

4 0
3 years ago
Read 2 more answers
What is the distance between (1, -4) and (1, 18​
Annette [7]
<h3>Answer: 22 units</h3>

=====================================================

Explanation:

You can use the distance formula

d = \sqrt{ (x_1-x_2)^2 + (y_1-y_2)^2}\\\\d = \sqrt{ (1-1)^2 + (-4-18)^2}\\\\d = \sqrt{ (0)^2 + (-22)^2}\\\\d = \sqrt{ 22^2}\\\\d = 22\\\\

----------------

A shorter method is to subtract the y coordinates and apply absolute value

So either |-4-18| = |-22| = 22

Or, |18 - (-4)| = |18+4| = |22| = 22

This method only works because the x coordinates are the same. We can also use this method if the y coordinates were the same with the x coordinates being different.

4 0
3 years ago
1 1/3 ÷ 5/6 qual e a resposta dessa pergunta<br><br><br>​
Korvikt [17]

Answer: 1 9/15

Step-by-step explanation:

I can’t speak Spanish

6 0
3 years ago
Fill the missing values in the ratio table
kramer

Answer:

A really out of focus picture, but I think this might be what you want.

Step-by-step explanation:

8 0
2 years ago
What is the product?
nirvana33 [79]

Answer:

the answer is B

Step-by-step explanation:

^^

8 0
2 years ago
Other questions:
  • I have another question if anyone is willing to help out.Number 4
    11·1 answer
  • Mason has 108 feet of material to build a fence around a rectangular pool on his property. If the width of the fence must be 6 f
    5·2 answers
  • jesse, meg and kelly each ate 0.32 of a pizza pie. what's the best estimate of how much of the pie they ate together
    12·2 answers
  • What is the value of Y?
    11·1 answer
  • (Best answer gets brainliest, Good answers get 5 stars, all answers get thanks.)
    8·2 answers
  • Solve the equation for Y<br> 2x + y = -9
    7·2 answers
  • Mason used 1/5 of a liter of water to fill 1/8 of an aquarium. How much water, in liters, is required to fill the aquarium?
    9·1 answer
  • Question 2: SQUARE ROOTS
    5·1 answer
  • Does anyone know the answer plz ?
    6·1 answer
  • A<br> LaDawn buys a ten-pack of gel pens for $7.50. How much did each pen<br> cost?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!