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3 years ago

SUB TO ME thunderoflight12 PLSSSSSSSSSSSSSSS I WILL MARK BRAINLYIST IF YOU DO FOR ALL MY THINGS

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Alona [7]3 years ago

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Answer:

done

Explanation:

BabaBlast [244]3 years ago

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I subscribe to you :)
Your welcome

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Show that the set of vectors {(−4,1,3),(5,1,6),(6,0,2)} does not span R 3 , but that it does span the subspace of R 3 consisting

Alika [10]

Answer:

The vectors does not span R3 and only span a subspace of R3 which satisfies x+13y-3z=0

Explanation:

The vectors are given as

$v_1=\left[\begin{array}{c}-4&1&3\end{array}\right] \\v_2=\left[\begin{array}{c}-5&1&6\end{array}\right] \\v_3=\left[\begin{array}{c}6&0&2\end{array}\right]$

Now if the vectors would span the $R^3$ , the rank of the consolidated matrix will be 3 if it is not 3 this indicates that the vectors does not span the $R^3$ .

So the matrix is given as

$M=\left[\begin{array}{ccc}v_1&v_2&v_3\end{array}\right] \\M=\left[\begin{array}{ccc}-4&5&6\\1&1&0\\3&6&2\end{array}\right]\\$

In order to calculate the rank, the matrix is reduced to the Row Echelon form as

$\approx \left[\begin{array}{ccc}-4&5&6\\ 0&\frac{9}{4}&\frac{3}{2}\\ 3&6&2\end{array}\right] R_2 \rightarrow R_2+\frac{R_1}{4}$

$\approx \left[\begin{array}{ccc}-4&5&6\\ 0&\frac{9}{4}&\frac{3}{2}\\ 0&\frac{39}{4}&\frac{13}{2}\end{array}\right] R_3 \rightarrow R_3+\frac{3R_1}{4}\\$

$\approx \left[\begin{array}{ccc}-4&5&6\\ 0&\frac{39}{4}&\frac{13}{2\\ 0&\frac{9}{4}&\frac{3}{2}}\end{array}\right] R_2\:\leftrightarrow \:R_3$

$\approx \left[\begin{array}{ccc}-4&5&6\\ 0&\frac{39}{4}&\frac{13}{2}\\ 0&0&0\end{array}\right] R_3 \rightarrow R_3-\frac{3R_2}{13}\\$

As the Rank is given as number of non-zero rows in the Row echelon form which are 2 so the rank is 2.

Thus this indicates that the vectors does not span $R^3$

Now for any vector the corresponding equation is formulated by using the combined matrix which is given as for any arbitrary vector and the coordinate as

$v=\left[\begin{array}{c}x&y&z\end{array}\right]$

$c=\left[\begin{array}{c}c_1&c_2&c_3\end{array}\right]$

$Mc=v$

$\left[\begin{array}{ccc}-4&5&6\\1&1&0\\3&6&2\end{array}\right]\left[\begin{array}{c}c_1&c_2&c_3\end{array}\right]=\left[\begin{array}{c}x&y&z\end{array}\right]$

$M=\left[\begin{array}{ccccc}v_1&v_2&v_3& | &v\end{array}\right] \\M=\left[\begin{array}{ccccc}-4&5&6&|&x\\1&1&0&|&y\\3&6&2&|&z\end{array}\right]\\$

Now converting the combined matrix as

$\approx \left[\begin{array}{ccccc}-4&5&6&|&x\\ 0&\frac{9}{4}&\frac{3}{2}&|&\frac{4y+x}{4}\\ 3&6&2&|&z\end{array}\right] R_2 \rightarrow R_2+\frac{R_1}{4}\\$

$\approx \left[\begin{array}{ccccc}-4&5&6&|&x\\ 0&\frac{9}{4}&\frac{3}{2}&|&\frac{4y+x}{4}\\ 0&\frac{39}{4}&\frac{13}{2}&|&\frac{4z+3x}{4}\end{array}\right] R_3 \rightarrow R_3+\frac{3R_1}{4}\\$

$\approx \left[\begin{array}{ccccc}-4&5&6&|&x\\ 0&\frac{39}{4}&\frac{13}{2}&|&\frac{4z+3x}{4}\\ 0&\frac{9}{4}&\frac{3}{2}&|&\frac{4y+x}{4}\end{array}\right] R_3 \leftrightarrow R_2\\$

$\approx \left[\begin{array}{ccccc}-4&5&6&|&x\\ 0&\frac{39}{4}&\frac{13}{2}&|&\frac{4z+3x}{4}\\ 0&0&0&|&\frac{13y+x-3z}{13}\end{array}\right] R_3 \rightarrow R_3-\frac{3R_2}{13}\\$

From this it is seen that whatever the values of the coordinates does not effect the value of the plane with equation as

$\frac{13y+x-3z}{13}=0\\or\\13y+x-3z=0\\$

So it is verified that the subspace of R3 such that it satisfies x+13y-3z=0 consists of all vectors.

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3 years ago

Explain the importance of international employment

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Answer:

having international workers allow organisation to be connected two other country markets as well.they get to know the best places to get resources and how to approach different countries through being thought business norms and culture by international employees.

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3 years ago

What is perfect competition of economic

iris [78.8K]

- Free entry and exit
- Homogeneous product
- Large buyers and sellers
- No artificial restrictions
- No transportation costs
- Perfect knowledge of prices and technology

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3 years ago

A carpenter sells _______ , whereas an automobile manufacturer sells _______.

Scorpion4ik [409]

Basic Answer

a carpenter sells furniture, whereas an automobile manufacturer sells cars.

Bussiness Answer

a carpenter sells style , whereas an automobile manufacturer sells mobility.

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3 years ago

Arie is a team lead for a group of engineers working on a new product. Arie decides to assign four additional engineers to the p

Vlad1618 [11]

Answer:

B. managerial

Explanation:

When something involves activities of management is called managerial. In the example given this is the nature of the behavior because Arie is organizing and directing the corporation in order to optimize and be efficient.

I hope you find this information useful and interesting! Good luck!

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