Row Operator
Row Operator
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Row Operator
Math Matrix Questions (row operators)?
Find the inverse of the matrix A, using row operators
A =
1 - 2 3
2 3 0
2 2 1
1. What is the 3 × 6 augmented matrix [A | I].
2. Convert the 3 × 6 matrix to echelon form using row operations.
3. Continue, with row operations, to convert the left-hand side of the
matrix into the identity matrix.
4. What is the inverse of A.
I have the answers for these but I'm not 100% sure how thay came about. Any help would be good thanks
1. Easy! It's just this:
[ 1 -2 3 | 1 0 0 ]
[ 2 3 0 | 0 1 0 ]
[ 2 2 1 | 0 0 1 ]
2. Now it's a simple matter of gaussian elimination (row operations). First I'll subtract 2 times the first row from the second and third:
[ 1 -2 3 | 1 0 0 ]
[ 0 7 -6 | -2 1 0 ]
[ 0 6 -5 | -2 0 1 ]
I will now, for the sake of simplicity, multiply the second row by 6 and the third by 7:
[ 1 -2 3 | 1 0 0 ]
[ 0 42 -36 | -12 6 0 ]
[ 0 42 -35 | -14 0 7 ]
Now we can subtract the second row from the first:
[ 1 -2 3 | 1 0 0 ]
[ 0 42 -36 | -12 6 0 ]
[ 0 0 1 | -2 -6 7 ]
(Note: if you divide the second row by 42, you have echelon form!)
3. Let's simplify the second row back to where it was by dividing by 6:
[ 1 -2 3 | 1 0 0 ]
[ 0 7 -6 | -2 1 0 ]
[ 0 0 1 | -2 -6 7 ]
Add 6 times the bottom row to the second and subtract it 3 times from the first.
[ 1 -2 0 | 7 18 -21 ]
[ 0 7 0 | -14 -35 0 ]
[ 0 0 1 | -2 -6 7 ]
Now, of course, we divide the second row by 7:
[ 1 -2 0 | 7 18 -21 ]
[ 0 1 0 | -2 -5 0 ]
[ 0 0 1 | -2 -6 7 ]
And finally, add 2 lots of the second row to the first:
[ 1 0 0 | 3 8 -21 ]
[ 0 1 0 | -2 -5 0 ]
[ 0 0 1 | -2 -6 7 ]
4. Hence the inverse is:
[ 3 8 -21 ]
[ -2 -5 0 ]
[ -2 -6 7 ]
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Row Operator
The Concept 2 Rowing Workout Equipment - A Review of Unique Features by Ross Mayer
Concept 2 rowing workout machines began making their appearance several decades ago in 1981. They are manufactured and shipped from Vermont, and the company developed this rower just because they were so aware of the need to train in the winter. So it figures that creating a high quality rowing machine for use indoors would be a great idea. Another serious concern was the desire to create the very best using the highest standards for design and materials. As someone who has tried their rowing machines, I can attest to the fact that their machines work well. I will share details touching on the more notable qualities of this workout equipment.
You will find two models available, the Model D and E. But, the Model D rower can be bought with separate options depending on your requirements. EveryEvery last rowing machine typically comes with a performance monitor of which there are two types, the PM3 and PM4. The Model D is shipped with a PM3, but you can upgrade to a PM4 at additional cost. The higher priced Model E always includes the PM4 with it as the main performance monitor. The Model D has the lowest pricetag of $900 and higher price with the better monitor.
You will be able to track how well you are doing with the performance monitors as well as monitoring your pulse rate. The way you can do that with the pulse is with an additional small device that you wear across your chest area. You may think heart rate monitor will be noticeable and make you incomfortable, but that isn't true. The moment you you go rowing you will hardly notice you've got a monitor strapped across your chest. The heart rate monitor is also a wireless device, so that means no wires are going to be swinging off of you.
The resistance to rowing is accomplished by utilizing an intelligently designed flywheel that is much like a manual fan. There are no safety issues with this as the flywheel is completely encased in a plastic assembly. You can set the amount of resistance with a small lever on the flywheel housing. When you are rowing you will hear the seat go back and forth, the chain movement and the whirringwhizzing of wind from the flywheel, and the noise level is very low. During rowing operations, the fan-like flywheel lets out a quiet sound, and you can feel the air movement at certain angles. However, I can tell you after many years of use that the flywheel movement is not at all distracting. All in all, you could easily use a Concept 2 rowing machine in the next room without waking up other people.
Either performance monitor also allows you to track different types of data about your rowing in real time. Just a few of the available rowing metrics include total rowing time, total distance rowed, 500 meter split times and number of strokes per minute. Your particular needs will help you figure out what you want to keep track of and what is not so important. This mainly concerns whether you are rowing for general fitness, or if you row competitively and what level you enter in.
About the Author
Ross' websites: Courier Tracking Software Installation, Tracking Shipments With GPS, SNCF-Holidays in France and The French Rail Network of SNCF.
Row Operator
Sade - Smooth Operator - LIVE FRONT ROW CENTER - August 6, 2011
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