If x = 4, y = 2 and z = 1 then xz (4y

Prove that if the set of vectors {u1, u2, u3} is linearly dependent and u4 is any vector, then the set {u1, u2, u3, u4} is linea

Lesechka [4]

Answer with Step-by-step explanation:

We are given that the set of vectors ${u_1,u_2,u_3}$ is lineraly dependent set .

We have to prove that the set ${u_1,u_2,u_3,u_4}$ is linearly dependent .

Linearly dependent vectors : If the vectors $u_1,u_2.u_3,u_4$

are linearly dependent therefore the linear combination

$a_1u_1+a_2u_2+a_3u_3+a_4u_4=0$

Then ,there exit a scalar which is not equal to zero .

Let $a_1\neq0$ then the vector $u_1$ will be zero and remaining other vectors are not zero.

Proof:

When $u_1,u_2,u_3$ are linearly dependent vectors therefore, linear combination of vectors of given set

$a_1u_1+a_2u_2+a_3u_3=0$

By definition of linearly dependent vector

There exist a scalar which is not equal to zero.

Suppose $a_1\neq 0$ then $u_1=0$

The linear combination of the set ${u_1,u_2,u_3,u_4}$

$a_1u_1+a_2u_2+a_3u_3+a_4u_4=0$

When $a_1\neq0\; and\; u_1=0$

Therefore,the set ${u_1,u_2,u_3,u_4}$ is linearly dependent because it contain a vector which is zero.

Hence, proved .

5 0

3 years ago

Dan is completing a 60-kilometer run. The diagram below shows what percent he has run so far.

dedylja [7]

Answer:20

Step-by-step explanation:

i got it right in my dca

4 0

3 years ago

Two of the statements are true; one is a lie.

Reptile [31]

Answer:

Step-by-step explanation:

The last statement is false.

∠BAF and ∠EAB are supplementary angles.

8 0

3 years ago

Vera is an ecologist who studies the change in the bear population of Siberia over time. The relationship between the elapsed ti

rewona [7]

Answer:

Every year, the bear population shrinks by a factor of 2/3 .

Explanation:

The concrete question and the function or data were omitted.

I found the complete question on the internet. Please, find attached the picture with the complete question

You must complete the sentence about the yearly rate of change of the bear population, telling whether it grows or shrinks and by what factor.

Thus, the goal is to interpret the rate of change in an exponential model.

The exponential model is:

$N(t)=2187\cdot \bigg(\dfrac{2}{3}\bigg)^t$

Let's analyze that function.

When t = 0, (2/3)⁰ = 1 and N(0) = 2,187 × 1 = 2,187

Thus, the population of bears starts with 2,187 individuals.

For t = 1, the population will be N(1) = 2,187 × (2/3).

For t = 2, the population will be N(2) = 2,187 × (2/3)²

And so on, every year the population of bears is multiplied by a factor of 2/3.

Since, 2/3 is less than 1, every year the population will be decreasing (decaying), by a factor of 2/3.

Thus, the answer, i.e. the complete sentence, is:

Every year, the bear population shrinks by a factor of 2/3 .

6 0

4 years ago

Read 2 more answers

If a= -1,-3 and b= 11, -8 what is the length of ab

Elza [17]

Answer:

its 13 units i just took it on ap3X

Step-by-step explanation:

7 0

3 years ago

If x = 4, y = 2 and z = 1 then xz (4y - 2z) is