## how do you reduce a matrix wtih variables to rref?

Linear spaces and subspaces, linear transformations, bases, etc.
king&i
Posts: 23
Joined: Sat Mar 07, 2009 5:13 pm

### how do you reduce a matrix wtih variables to rref?

how do u reduce a matrix wtih variables to rref?
0 2 2
1 h 0
-2 7 h

Martingale
Posts: 333
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
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### Re: how do you reduce a matrix wtih variables to rref?

how do u reduce a matrix wtih variables to rref?
0 2 2
1 h 0
-2 7 h
the same way you do it when there are just numbers.

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
To expand upon the previous (completely correct) reply, you would use the exact same steps as you've always used (such as when you were, in another thread, finding the inverse of a matrix). The only difference is that you won't be able to simplify as much, between steps, due to the variable.

You have:
```[ 0 2 2 ]
[ 1 h 0 ]
[-2 7 h ]```
A good start would probably be to multiply the second row by 2, and add this to the third row, creating a new third row:
```2*R2 + R3 -> R3

[ 0    2 2 ]
[ 1    h 0 ]
[ 0 7+2h h ]```
Obviously, dividing the first row through by 2 would be helpful!
```(1/2)R1 -> R1

[ 0    1 1 ]
[ 1    h 0 ]
[ 0 7+2h h ]```
Then try multiplying the first row by -(7 + 2h), and adding the result to the third row. Also, multiply the first row by -h, and adding the result to the second row. Once you simplify, you can reorder the rows, and you should have your answer.

king&i
Posts: 23
Joined: Sat Mar 07, 2009 5:13 pm

### Re: how do you reduce a matrix wtih variables to rref?

so iw ould get

0 1 1
1 0 -h
0 0 -7-h

how do u no 2 do those steps?

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
so iw ould get

0 1 1
1 0 -h
0 0 -7-h
Now divide the third row by -7 - h, and the third row should look very nice.

Follow that up by subtracting the third row from the first row, and adding the product of h and the third row to the second row. Then swap the first and second rows.
how do u no 2 do those steps?
You don't! There is no one "sacred" "right" way of working toward reduced-row-echelon form. Each person does the step will seems easiest or most convenient for him, according to his current inclination. In a give group of a half-dozen students, you could see a half-dozen different sets of steps. As long as each step was mathematically valid, all half-dozen answers will be the same. And then if you asked them to do the same exercise the next day, their inclincations might be different, and you'd get a new set of steps from each!

Don't worry about "the" right way. Just make sure you're careful with your arithmetic, do your work clearly, and are doing what makes sense to you!