Reduced Row Echelon Form and Row Operations - Linear Algebra
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Use row operations to find the inverse of the matrix 
Use row operations to find the inverse of the matrix
add the first row to the second
subtract two times the second row to the first
subtract the last row from the top row
subtract the first row from the last row
subtract two times the last row from the second row
switch the sign in the middle row

The inverse is 
add the first row to the second
subtract two times the second row to the first
subtract the last row from the top row
subtract the first row from the last row
subtract two times the last row from the second row
switch the sign in the middle row
The inverse is
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Find the inverse using row operations

Find the inverse using row operations
To find the inverse, use row operations:
add the third row to the second
subtract the second row from the top
subtract the first row from the second
subtract two times the first row from the bottom row
subtract three times the bottom row from the second row
subtract 2 times the middle row from the bottom row
add the bottom row to the top

The inverse is 
To find the inverse, use row operations:
add the third row to the second
subtract the second row from the top
subtract the first row from the second
subtract two times the first row from the bottom row
subtract three times the bottom row from the second row
subtract 2 times the middle row from the bottom row
add the bottom row to the top
The inverse is
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Find the inverse using row operations: 
Find the inverse using row operations:
subtract two times the second row from the last row
subtract the second row from the first
subtract two times the first row from the second
add the third row to the second
subtract 7 times the second row from the third row, then multiply by -1
add the bottom row to the middle row
add the last row to the top row
subtract two times the second row from the top row

The inverse is

subtract two times the second row from the last row
subtract the second row from the first
subtract two times the first row from the second
add the third row to the second
subtract 7 times the second row from the third row, then multiply by -1
add the bottom row to the middle row
add the last row to the top row
subtract two times the second row from the top row
The inverse is
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Change the following matrix into reduced row echelon form.

Change the following matrix into reduced row echelon form.
In order to get the matrix into reduced row echelon form,
Multiply the first row by 

Add
times row one to row 2

Multiply the second row by 

Add -
times row two to row one

In order to get the matrix into reduced row echelon form,
Multiply the first row by
Add times row one to row 2
Multiply the second row by
Add - times row two to row one
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Change the following matrix into reduced row echelon form.

Change the following matrix into reduced row echelon form.
Multiply row one by 

Add
times row one to row two

Multiply row two by 

Add
times row two to row one.

Multiply row one by
Add times row one to row two
Multiply row two by
Add times row two to row one.
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Compare your answer with the correct one above
Compare your answer with the correct one above
Compare your answer with the correct one above
Compare your answer with the correct one above
Compare your answer with the correct one above
Compare your answer with the correct one above
Compare your answer with the correct one above
Compare your answer with the correct one above
Compare your answer with the correct one above
Compare your answer with the correct one above
Compare your answer with the correct one above
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Give the elementary matrix that represents performing the row operation

in solving a three-by-three linear system.
Give the elementary matrix that represents performing the row operation
in solving a three-by-three linear system.
The elementary matrix that represents a row operation is the result of performing the same operation on the appropriate identity matrix - which here is the three-by-three matrix
. The row operation
is the multiplication of each element of in the second row of an augmented matrix by the scalar
, so do this to the identity:


This is the correct response.
The elementary matrix that represents a row operation is the result of performing the same operation on the appropriate identity matrix - which here is the three-by-three matrix . The row operation
is the multiplication of each element of in the second row of an augmented matrix by the scalar
, so do this to the identity:
This is the correct response.
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Which of the following is an example of an elementary matrix?
Which of the following is an example of an elementary matrix?
An elementary matrix is one that can be formed from the (here, three-by-three) identity matrix

by way of exactly one row operation. An elementary matrix can have one of the following characteristics:
- Exactly two rows are switched. The only choice that repositions rows is
,
but this choice rearranges all three rows, so this is incorrect.
- All of the "1" elements in the diagonal remain unchanged, but exactly one "0" is changed to a nonzero number. The choice that leaves all "1" elements unchanged is

but this matrix changes two of the zeroes to nonzero elements.
- One of the "1" elements in the diagonal is changed to another nonzero element. The other three choices change these elements. But, of them:

changes two of the "1" elements to other nonzero numbers, and

also changes a "0" to a nonzero number.
,
however, makes one such change and no others, so it is an elementary matrix, and it is the correct choice.
An elementary matrix is one that can be formed from the (here, three-by-three) identity matrix
by way of exactly one row operation. An elementary matrix can have one of the following characteristics:
- Exactly two rows are switched. The only choice that repositions rows is
,
but this choice rearranges all three rows, so this is incorrect.
- All of the "1" elements in the diagonal remain unchanged, but exactly one "0" is changed to a nonzero number. The choice that leaves all "1" elements unchanged is
but this matrix changes two of the zeroes to nonzero elements.
- One of the "1" elements in the diagonal is changed to another nonzero element. The other three choices change these elements. But, of them:
changes two of the "1" elements to other nonzero numbers, and
also changes a "0" to a nonzero number.
,
however, makes one such change and no others, so it is an elementary matrix, and it is the correct choice.
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Which of the following elementary matrices represents the row operation

on a four-by-four system?
Which of the following elementary matrices represents the row operation
on a four-by-four system?
An elementary matrix is one that can be formed from the (here, four-by-four) identity matrix

by way of exactly one row operation.
represents the addition of
times each element in Row 1 to the corresponding element in Row 4, so do this in the identity matrix:

,
the correct choice.
An elementary matrix is one that can be formed from the (here, four-by-four) identity matrix
by way of exactly one row operation. represents the addition of
times each element in Row 1 to the corresponding element in Row 4, so do this in the identity matrix:
,
the correct choice.
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