Answer:
License: legal permission to work granted by the government
Associated degree: general two-year college-level degree
Career college: a one or two-year program ending with a certificate
Bachelor's degree: four-year college level degree
Apprenticeship: an on-the-job training experience
Explanation:
<u>License:</u> legal permission to work granted by the government
<u>Associated degree:</u> general two-year college-level degree
<u>Career college also called vocational school:</u> a one or two-year program ending with a certificate
<u>Bachelor's degree:</u> four-year college level degree
<u>Apprenticeship:</u> an on-the-job training experience
Answer:
(a) $5,690
(b) $380
Explanation:
Given that,
current assets = $2,090
Net fixed assets = $9,830
Current liabilities = $1710
Long-term debt = $4520
Total assets:
= Current assets + Net fixed assets
= $2,090 + $9,830
= $11,920
Total Liabilities:
= Current Liabilities + Long-term Debt
= $1710 + $4520
= $6,230
(a) Total assets = Total liabilities + Stockholder's equity
$11,920 = $6,230 + Stockholder's equity
$11,920 - $6,230 = Stockholder's equity
$5,690 = Stockholder's equity
(b) Net working capital:
= Current assets - Current liabilities
= $2,090 - $1,710
= $380
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>
<em />![v=\left[\begin{array}{c}x&y&z\end{array}\right]](https://tex.z-dn.net/?f=v%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%26y%26z%5Cend%7Barray%7D%5Cright%5D)
<em />
<em />![c=\left[\begin{array}{c}c_1&c_2&c_3\end{array}\right]](https://tex.z-dn.net/?f=c%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dc_1%26c_2%26c_3%5Cend%7Barray%7D%5Cright%5D)
<em />
<em />
<em />
<em />![\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]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%265%266%5C%5C1%261%260%5C%5C3%266%262%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dc_1%26c_2%26c_3%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%26y%26z%5Cend%7Barray%7D%5Cright%5D)
<em />
<em />![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]\\](https://tex.z-dn.net/?f=M%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7Dv_1%26v_2%26v_3%26%20%7C%20%26v%5Cend%7Barray%7D%5Cright%5D%20%5C%5CM%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D-4%265%266%26%7C%26x%5C%5C1%261%260%26%7C%26y%5C%5C3%266%262%26%7C%26z%5Cend%7Barray%7D%5Cright%5D%5C%5C)
<em />
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.
<em />
Answer:
<h3>B. provide financial services to customers at no cost.</h3>
Explanation:
i hope it helps :)
