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]](https://tex.z-dn.net/?f=v_1%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-4%261%263%5Cend%7Barray%7D%5Cright%5D%20%5C%5Cv_2%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-5%261%266%5Cend%7Barray%7D%5Cright%5D%20%5C%5Cv_3%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D6%260%262%5Cend%7Barray%7D%5Cright%5D)
Now if the vectors would span the
, the rank of the consolidated matrix will be 3 if it is not 3 this indicates that the vectors does not span the
.
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]\\](https://tex.z-dn.net/?f=M%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dv_1%26v_2%26v_3%5Cend%7Barray%7D%5Cright%5D%20%5C%5CM%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%265%266%5C%5C1%261%260%5C%5C3%266%262%5Cend%7Barray%7D%5Cright%5D%5C%5C)
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}](https://tex.z-dn.net/?f=%5Capprox%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%265%266%5C%5C%200%26%5Cfrac%7B9%7D%7B4%7D%26%5Cfrac%7B3%7D%7B2%7D%5C%5C%203%266%262%5Cend%7Barray%7D%5Cright%5D%20R_2%20%5Crightarrow%20R_2%2B%5Cfrac%7BR_1%7D%7B4%7D)
![\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}\\](https://tex.z-dn.net/?f=%5Capprox%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%265%266%5C%5C%200%26%5Cfrac%7B9%7D%7B4%7D%26%5Cfrac%7B3%7D%7B2%7D%5C%5C%200%26%5Cfrac%7B39%7D%7B4%7D%26%5Cfrac%7B13%7D%7B2%7D%5Cend%7Barray%7D%5Cright%5D%20R_3%20%5Crightarrow%20R_3%2B%5Cfrac%7B3R_1%7D%7B4%7D%5C%5C)
![\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](https://tex.z-dn.net/?f=%5Capprox%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%265%266%5C%5C%200%26%5Cfrac%7B39%7D%7B4%7D%26%5Cfrac%7B13%7D%7B2%5C%5C%200%26%5Cfrac%7B9%7D%7B4%7D%26%5Cfrac%7B3%7D%7B2%7D%7D%5Cend%7Barray%7D%5Cright%5D%20R_2%5C%3A%5Cleftrightarrow%20%5C%3AR_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}\\](https://tex.z-dn.net/?f=%5Capprox%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%265%266%5C%5C%200%26%5Cfrac%7B39%7D%7B4%7D%26%5Cfrac%7B13%7D%7B2%7D%5C%5C%200%260%260%5Cend%7Barray%7D%5Cright%5D%20R_3%20%5Crightarrow%20R_3-%5Cfrac%7B3R_2%7D%7B13%7D%5C%5C)
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 
<em>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 </em>
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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}\\](https://tex.z-dn.net/?f=%5Capprox%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D-4%265%266%26%7C%26x%5C%5C%200%26%5Cfrac%7B9%7D%7B4%7D%26%5Cfrac%7B3%7D%7B2%7D%26%7C%26%5Cfrac%7B4y%2Bx%7D%7B4%7D%5C%5C%203%266%262%26%7C%26z%5Cend%7Barray%7D%5Cright%5D%20R_2%20%5Crightarrow%20R_2%2B%5Cfrac%7BR_1%7D%7B4%7D%5C%5C)
![\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}\\](https://tex.z-dn.net/?f=%5Capprox%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D-4%265%266%26%7C%26x%5C%5C%200%26%5Cfrac%7B9%7D%7B4%7D%26%5Cfrac%7B3%7D%7B2%7D%26%7C%26%5Cfrac%7B4y%2Bx%7D%7B4%7D%5C%5C%200%26%5Cfrac%7B39%7D%7B4%7D%26%5Cfrac%7B13%7D%7B2%7D%26%7C%26%5Cfrac%7B4z%2B3x%7D%7B4%7D%5Cend%7Barray%7D%5Cright%5D%20R_3%20%5Crightarrow%20R_3%2B%5Cfrac%7B3R_1%7D%7B4%7D%5C%5C)
![\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\\](https://tex.z-dn.net/?f=%5Capprox%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D-4%265%266%26%7C%26x%5C%5C%200%26%5Cfrac%7B39%7D%7B4%7D%26%5Cfrac%7B13%7D%7B2%7D%26%7C%26%5Cfrac%7B4z%2B3x%7D%7B4%7D%5C%5C%200%26%5Cfrac%7B9%7D%7B4%7D%26%5Cfrac%7B3%7D%7B2%7D%26%7C%26%5Cfrac%7B4y%2Bx%7D%7B4%7D%5Cend%7Barray%7D%5Cright%5D%20R_3%20%5Cleftrightarrow%20R_2%5C%5C)
![\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}\\](https://tex.z-dn.net/?f=%5Capprox%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D-4%265%266%26%7C%26x%5C%5C%200%26%5Cfrac%7B39%7D%7B4%7D%26%5Cfrac%7B13%7D%7B2%7D%26%7C%26%5Cfrac%7B4z%2B3x%7D%7B4%7D%5C%5C%200%260%260%26%7C%26%5Cfrac%7B13y%2Bx-3z%7D%7B13%7D%5Cend%7Barray%7D%5Cright%5D%20R_3%20%5Crightarrow%20R_3-%5Cfrac%7B3R_2%7D%7B13%7D%5C%5C)
From this it is seen that whatever the values of the coordinates does not effect the value of the plane with equation as

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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Answer:
Idea generation
Explanation:
Idea generation -
It is the method for searching new methodology or technique to the solution to any previous idea .
It is the main and the most primary focus during the phase of the creative process .
Analyzing the market , interpreting the competitions and asking the customers , all falls in this stage .
Hence , the stage which is asked by the question data is the stage of Idea generation .
Answer: An entrepreneur
Explanation: An entrepreneur is an individual who takes the risk of opening a new business from nothing. An entrepreneur takes the risk to nurture a business from it's early days upto when the business fully takes shape.
Angelina is a typical example of an entrepreneur taking the risk of leaving her paid job to open a business from scratch, bearing all the risks involved in setting up a business.
Answer:
D) M1 falls by $1,000, and M2 is unchanged.
Explanation:
since checking account comes under M1, a transfer would result in fail, Therefore, a transfer would result in a change in M1 but shows no effect on M2
Answer:
17%
Explanation:
If a company issued a short-term note payable to a bank with a stated 12 percent rate of interest and in addition the bank charged a .5% loan origination fee and remitted the balance to the company. The effective interest rate paid by the company in this transaction would be 17%
The effective annual interest rate is <u>the interest rate that is actually earned or paid on an investment, loan</u> or other financial product.
Hence, since the company is both paying the initial 5% and the later 12%, effectively the company is paying 17% on the note payable.