Essie S.

asked • 02/19/17

Find elementary matrices such that E1A= B

A= [2 -1 4]
[ 3 1 -1]
[ 4 2 1 ]

B= [ 2 -1 4 ]
[ 3 1 -1 ]
[ 0 4 -7 ]

Please explain me the steps. I dont understand what I have to do. 

1 Expert Answer

By:

Mark M. answered • 02/19/17

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In A, multiply row 1 by 2 and subtract that from row 3. The results is B.
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Essie S.

Thank you. Just one last questiom, in my solutions booklet it shows E1= [ 1 0 0 ]
                               [ 0 1 0 ] 
                               [ -2 0 1 ] 
 
Where does this answer come from ?How do I get it?
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02/19/17

Mark M.

| 1  0 0 |     | 2 -1 4 |     | 2 -1 4 |
| 0  1 0 |  • | 3  1 -1 | = | 3  1 -1 |
|-2  0 1 |    | 4  2  1 |     | 0 4  -7 |
 
Note that the row 3 in E only changes row 3 in A by multiply row 1 and adding it to row 3.
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02/19/17

Essie S.

I still dont get it. The operation I did to make it look like B is Row3-2Row1 . After this what do I do? I stilll dont get how the book got that matrice i asked before
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02/19/17

Essie S.

Nvm I think I got it. So to get that matrice I just apply this row operation r3 -2r1 to the identity matrice ?
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02/19/17

Mark M.

Your seeing the identity matrix is a start. The only operation to be done is multiplying row 1 by -2 (that is the -2 in the lower left) and not modifying - that is the identity part.
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02/19/17

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