# Linear Algebra : Reduced Row Echelon Form and Row Operations

## Example Questions

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### Example Question #1 : Reduced Row Echelon Form And Row Operations

Use row operations to find the inverse of the matrix

Explanation:

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

The inverse is

### Example Question #2 : Reduced Row Echelon Form And Row Operations

Find the inverse using row operations

Explanation:

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

### Example Question #3 : Reduced Row Echelon Form And Row Operations

Find the inverse using row operations:

Explanation:

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

### Example Question #4 : Reduced Row Echelon Form And Row Operations

Change the following matrix into reduced row echelon form.

Explanation:

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

### Example Question #1 : Reduced Row Echelon Form And Row Operations

Change the following matrix into reduced row echelon form.

Explanation:

Multiply row one by

Add  times row one to row two

Multiply row two by

Add  times row two to row one.

Explanation:

Explanation:

Explanation:

Explanation: