how do u reduce a matrix wtih variables to rref?

0 2 2

1 h 0

-2 7 h

how do u reduce a matrix wtih variables to rref?

0 2 2

1 h 0

-2 7 h

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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the same way you do it when there are just numbers.how do u reduce a matrix wtih variables to rref?

0 2 2

1 h 0

-2 7 h

- stapel_eliz
**Posts:**1628**Joined:**Mon Dec 08, 2008 4:22 pm-
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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:

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.

so iw ould get

0 1 1

1 0 -h

0 0 -7-h

how do u no 2 do those steps?

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-
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Now divide the third row by -7 - h, and the third row should look very nice.so iw ould get

0 1 1

1 0 -h

0 0 -7-h

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.

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!how do u no 2 do those steps?

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