anyone?
Can someone help me solve this systems of equations problem using a matrix and in reduced row echelon form:
3x-y+z=10
2x-4y-z=20
6x+8y+z=-100
i got the answers to be x: -6, y=-8, and z=0
i need help,though, on how to complete this problem without a calculator, like a walk through. any help would be greatly appreciated
i have it set up here
"i got the answers to be x: -6, y=-8, and z=0"
These answers are totally wrong!!!
To check the answers, just sub their respective values inside each of the equations...Here's the workings i have written manually...Please click on the attached file and click on it again and then zoom in to have a better view.But my workings are rather long though and besides, u can just use mental calculation^_^ without using calculator
Hi,
With a system of equations you can add multiples of one equation to another. This way you can find a solution much quicker than you have already.
For example, if you multiply your first equation by 2 you get 6x-2y+2z=20.
if you subtract this equation from the 3rd equation you get 6y+z=120.
By continuing this process you will eventually reduce an equation with just one unknown. You should be able to do this after 2 or 3 steps.
The other method (which in principle is identical to this approach) is to represent the system of equations into a matrix and do what is called "gaussian elimination" which is a smart approach to take - have a look on the net for a description.
Hope this helps!
to get an upper triangular form of the matrix
1) keep row one
subtract/add multiples of this row to achieve zeros in the rest of column one
2) keep row 2
subtract/add multiples of this row to achieve zeros in the rest of column two
1) in this case R2-2/3R1
R3-2R1
2) R3+3R2
GIVES 3 -1 1 : 10
0 -10/3 -5/3 :40/3
0 0 -6 : 40
-6Z = 40
Z=20/3 SO Y = -22/3 SO X = -4/3
Hope my arithmetic is right!
I know that i can use Gaussian elimination but I'm supposed to solve it with a 3x4 matrix or else i would have had it done a loooooooong time ago
this is the goal for the problem
1 0 0 : x
0 1 0 : y
0 0 1 : z
also sorry, I do see the mistake I made it is supposed to be:
3 -1 1 : -10
2 -4 -1 : 20
6 8 1 :-100
He gives a detailed solution. See Solution matrix - Calculator Online - Calculator-online.org