All categories

3 years ago

Suppose v1 , v2 , v3 ,v4 are vectors in R3.

Mathematics

1 answer:

mestny [16]3 years ago

5 0

Answer:

a. These four vectors are dependent because there are columns of 3 by 4 matrix with one free variable.

b. If one is a multiple of other

c. c1v1 + c20 = 0 has nontrivial solution.

Step-by-step explanation:

Any set of 4 or more vectors must be linearly dependent. The non trivial combination of vector may produce zero as the set is linearly dependent. The vector v1 and v2 will be dependent if one is the multiple of the other.

You might be interested in

Simplify the Polynomial and please show your work so I can do more on my own.

zheka24 [161]

Answer:

Step-by-step explanation:

7 0

3 years ago

Given points A (0,0), B (4,0), C (0,2), D (0,0), E (2,0), and F (0,1), which of the following proves that

damaskus [11]

Similar triangles may or may not have equal side lengths

Triangles ABC and DEF are similar by SSS theorem

<h3>How to determine the similarity statement</h3>

The coordinates of the two triangles are:

A (0,0), B (4,0), C (0,2), D (0,0), E (2,0), and F (0,1)

Calculate the lengths of both triangles using the following distance formula

$d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}$

For triangle ABC, we have:

$AB = \sqrt{(0 -4)^2 + (0 -0)^2} = 4$

$BC = \sqrt{(4 -0)^2 + (0 -2)^2} = 2\sqrt 5$

$CA = \sqrt{(0 -0)^2 + (0 -2)^2} = 2$

For triangle DEF, we have:

$DE = \sqrt{(0 -2)^2 + (0 -0)^2} = 2$

$EF = \sqrt{(2 -0)^2 + (0 -1)^2} = \sqrt 5$

$FD = \sqrt{(0 -0)^2 + (1 -0)^2} = 1$

Divide corresponding sides of the triangles to calculate the scale factor k

$k = \frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD}$

This gives

$k = \frac{4}{2} = \frac{2\sqrt 5}{\sqrt 5} = \frac{2}{1}$

Evaluate the quotients

$k = 2 = 2 = 2$

Since the quotients are equal, then the triangles are similar

Hence, triangles ABC and DEF are similar by SSS theorem

Read more about similar triangles at:

brainly.com/question/14285697

3 0

2 years ago

The cast of the play makes 275 programs for 5 shows. How many programs will be needed for 13 shows?

Advocard [28]

715 because 275/5= 55 then 55x13 will give you 715

8 0

3 years ago

Will give Brainly if correct

KengaRu [80]

Answer: -8

Step-by-step explanation: When it says f(x), all you have to do is find value x on the coordinate plane and look up or down until you find a point that runs through that x value. In this case, if you draw a line on x=5, you can see that it goes across a point that has a y value of -8, which is your answer.

8 0

3 years ago

HELP

Yakvenalex [24]

Answer:

5. 50.3 m²

6. 113.1 cm²

7. 102.1 yards²

8. 50.3 yards²

9. 452.2 ft²

10.379.8 ft²

Step-by-step explanation:

Area of a circle = nr²

The circumference of a circle = 2nr

n = pi = 22/7

r = radius

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

A radius is half of the diameter

radius = diameter / 2

5. (22/7) x 4² = 50.3 m²

6. (22/7) x 6² =113.1 cm²

7. radius = 11.4/2 = 5.7 yards

(22/7) x 5.7² =102.1 yards²

8. radius = 8/2 = 4 yards

(22/7) x 4² = 50.3 yards²

9. 2nr = 75.4 yards

2 x (22/7) x r = 75.4

to find r, divide both sides of the equation by 2 and 7/22

r = 12 ft

Area = (22/7) x 12² = 452.2 ft²

10. 2nr = 69.1 yards

2 x (22/7) x r = 69.1

to find r, divide both sides of the equation by 2 and 7/22

r = 10.99 ft²

Area = (22/7) x 10.99² = 379.8 ft²

the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero

8 0

3 years ago