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Use the reduced row echelon form function on your calculator
Shouldnt say me only O.o
Okay, so yeah, matricies business. So what I want to do is write this in matrix form. Writing it in that form is very straightforward. You just basically take the coefficients of everything and put them in a box, lol. The answers go in a separate box.....youll see what I mean and youll get how I set it up :3 |dw:1377832924126:dw|
t-89 will do it easy
So that is what we start with. Basically the coefficients of all the variables went, in order, in their own box and all the = to stuff went in its own box in order. So our goal when we're solving these is to gradually make the matrix look like this: |dw:1377833153644:dw| The x's arent important, I just put them there for filler. What is important is that we make a diagonal, from the top left to the bottom right, of 1's and the numbers underneath that line of ones we want to be 0.
So the way we go about this is called Gaussian elimination. Not that it matters, its row operations. The very first thing we have to do is make the topleft number a 1. It already is a 1, so yay us. Now what we do is basically a bunch of eliminations. Normally when we have a system of equations, like: 2x + 3y = 6 -x + y = 2 we would multiply the bottom row by 2 and we'd get x's to cancel and go from there. This is exactly what we're going to do. 2 rows at a time, we do a series of eliminations until the numbers we have remaining fit the form above. Now there is a bit of an order we have to do this in. We HAVE to use the first row in each elimination until we get the all the numbers in the left column like 1 0 0 0 So we start with row 1 and row 2 1 2 1 1 2 -3 -1 6 So now we must do elimination like we normally do and our goal is for that bottom left 2 to become 0. We can do this by doing the operation -2Row 1 + Row 2 (usually just written r sub 1, r sub 2, etc). So -2 R1 + R2 is -2 -4 -2 -2 2 -3 -1 6 --------------- 0 -7 -3 4 Now this result becomes our NEW row 2. We rip old the old row two and put this in its place. Row 1 DOES NOT change. We will keep row 1 like 1 2 1 1, only the row that we made 0 retains its new form. So this is quite a bit, so see if this makes sense first @Data_LG2
give me a sec. to understand this:)
so it will become like this?|dw:1377835412604:dw|
Yep, exactly. So now we do the same thing, but with row 1 and row 3 this time. So we would want to make the 3 in row 3 become a zero using: 1 2 1 1 3 5 4 5 So now we just do an elimination to make that 3 become 0. The result that we get after our elimination will replace row 3 in the same manner that we replaced row 2. Once again, the first row will not change.
it's only row 1 always??
Not always. We want the first COLUMN to look like 1 0 0 0 Once we achieve that, we stop using the first row.
ok.. i'll try it..
Alright, sure. Try to get the last two rows to be 0 and then ill help ya continue.
i got this|dw:1377836070934:dw|
That looks about right :3. So remember, we want this: |dw:1377836376910:dw| So the next thing we need to do is make that -7 into a positive 1. Now when you need a zero we have to do elimination. When we need a 1, we simply multiply or divide the row by whatever number gives us the desired 1. So multiply that row to make that -7 into a 1. Your whole row WILL change.
Right. So now the next step is to make that the two numbers -1 and -7 become 0s. This time we use row 2 both times in order to transform the numbers underneath it into 0's. So do you see what the next elimination step would be?
just add row 2 to row 3?
In this case yes, lo. Then your result becomes the new row 3.
Bingo. So now youll see the whole last row is eliminated and we have exactly what we want, a row with only on the left with only one non-zero number remaning. Now recall how I lined it up. The first COLUMN are all coefficients of x, the second COLUMN are all coefficients of y and the 3rd COLUMN are all coefficients of z. So if I tack all the variables back on: |dw:1377837247753:dw| As you can see, we basically have 10z/7 = 10/7. Given that, use the rows we have and solve for x y and z :3
WWWWWWOOOOOOOOOWWWWWW!!!!!!!!!!!!!!!!!!!!!!!!! thank you very much!!!!!
Lol, glad ya got it xDD
you're a good tutor:))))
Well as long as it makes sense what I did, then yeah :3
cool!... i can now do the other one by myself:) uhm.. are you doing physics too?
I took one physics class a few semesters ago.
so you're not doing it??? lol, just wondering.. i finish my calculus and vectors.. i'm studying physics right now:)
Ah. Nah, not doing it now. SO I may not know much. Maybe it looks familiar to me depending on what ya got xD
oh ok.. i'll ask you next time if i'll have problems:)
Alright, np :3