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makkiz [27]
4 years ago
13

Determine by inspection whether the vectors are linearly independent. Justify your answer.

Mathematics
1 answer:
jekas [21]4 years ago
7 0

Answer:

B. The set is linearly independent because at least one of the vectors is a multiple of another vector.

Step-by-step explanation:

A set of n vector of length n is linearly independent if the matrix with these vectors as column has none of zero determinant. The set of vectors is dependent if the determinant is zero. In the given question the vectors have no zero determinants therefore it is linearly independent.

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2. For the following, is the stated conclusion reasonable? Why or why not?
lapo4ka [179]

Answer:

Definetely, it is reasonable. You may assume that a pet as a companionship will help the elderly feel more comfortable and therefore, happy. There are a few problems tough:

  • There is no practical way of meassuring 'happiness'.
  • Sometimes, the correlations of two factors may be a coincidence. Scientist should always consider this when they try to claim something byusing some backup logic, like we did.
  • Even tough the statement makes some sense, you need to be aware that maybe is not completly positively correlated. Maybe having 20 more pets does not make an elderly happy if it alredy had 1 or 2.

8 0
3 years ago
Determine the number of real solutions of the equation. Then solve the equation using square roots
Kaylis [27]

Answer:

x ∉ R

Step-by-step explanation:

x² = - 21

if x² < 0 => x ∉ R

8 0
3 years ago
A group of winning ticket holders share equally 90,000,000 lottery. Before the money is divided, three more winning ticket holde
Kruka [31]

Let's assume

people were in the original group of winners as x

A group of winning ticket holders share equally 90,000,000 lottery

Before the money is divided, three more winning ticket holders are declared

so, total number of winning tickes =x+3

each persons share is reduced to 5,000,000

so, total money =5,000,000*(x+3)

and this must be equal to total money

5000000(x+3)=90,000,000

now, we can solve for x

and we get

x+3=18

Subtrac both sides by 3

x+3-3=18-3

x=15

so,

number of people were in the original group of winners is 15 ...........Answer

6 0
3 years ago
58:19
MakcuM [25]

Answer:

"Acceleration" means any change in the speed or direction of motion ... speeding up, slowing down, or turning.  So . . .

-- The distance traveled in a certain time may increase or decrease.

-- The displacement covered in a certain time may increase or decrease.

-- The speed of the object may increase or decrease.

-- The velocity of the object (speed/direction) will change.

Step-by-step explanation:

7 0
3 years ago
Pleaseeeeeee help mee
BlackZzzverrR [31]

Answer:

The solution of the given trigonometric equation

                   x = \frac{\pi }{6}

Step-by-step explanation:

<u><em>Step(i):</em></u>-

Given  

                cos( 3x - \frac{\pi }{3} )  = \frac{\sqrt{3} }{2}

                  cos( 3x - \frac{\pi }{3} )  = cos (\frac{\pi }{6} )

                      3x - \frac{\pi }{3}  =  \frac{\pi }{6}

                      3x - \frac{\pi }{3  } + \frac{\pi }{3}   =  \frac{\pi }{6} + \frac{\pi }{3}

                      3x = \frac{2\pi +\pi }{6} = \frac{3\pi }{6} = \frac{\pi }{2}

                     x = \frac{\pi }{6}

<u><em>Step(ii)</em></u>:-

The solution of the given trigonometric equation

                   x = \frac{\pi }{6}

<u><em>verification </em></u>:-

      cos( 3x - \frac{\pi }{3} )  = \frac{\sqrt{3} }{2}

put  x = \frac{\pi }{6}

    cos( 3(\frac{\pi }{6})  - \frac{\pi }{3} )  = \frac{\sqrt{3} }{2}

    cos (\frac{\pi }{6} ) = \frac{\sqrt{3} }{2} \\\\\frac{\sqrt{3} }{2} =  \frac{\sqrt{3} }{2}

Both are equal

∴The solution of the given trigonometric equation

                   x = \frac{\pi }{6}

                     

4 0
3 years ago
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