can someone please help me solve this question?
I tried so many times but I still could not get it...
x + y = 7
2x - y = 5
its supposed to start as
[1 1 | 7]
[2 -1 | 5].....
and the ans is supposed to be (4,3)
thanks in advance
much appreciated
There are 3 basic rules you can use on your matrix
1. you can interchange any two rows
2. you can multiply any row by a non-zero number
3. you can add/subtract a multiple of any row to any other row and replace the row with that result.
the idea is to make your matrix look like
1 0 a
0 1 b
then x=a
y=b
so for
1 1 7
2 -1 5
I will leave row 1 alone
row 2: 2xrow1 - row2
1 1 7
0 3 9
leave row1 alone
row2: divide by 3
1 1 7
0 1 3
row1: row1 - row2
leave row2 alone
1 0 4
0 1 3
now what does that matrix represent ?
1x + 0y = 4 , so x = 4
0x + 1y = 3 , so y = 3
Editorial:
Personally I think solving equations by matrix becomes an exercise in arithmetic manipulation.
Especially for an easy pair of 2 equations in 2 variables solving them this way is rather silly.
By the time somebody has solved one of these systems by the matrix method, I could have solved 3 or 4 systems by the old fashioned elimination method or in this case by substitution.
Hey ah kabdul. I did two of these Gauss Jordan things for you last night and Reiny did one now. Are you getting it? Try one yourself please and let us see if you can do it.
I do not like the method much by hand, but for large systems of equations that need to be solved methodically by computer programming this is the way to go, or used to be. The Fortran and octal programs I used to write are now incorporated in any old scientific calculator.
Ahh, Fortran
How things have changed.
I recall studying under Wesley Graham
at the University of Waterloo back in 1962
when he started to tweak Fortran and came up with several improved version of it, eventually becoming WatFor and WatBol (for Waterloo Fortran and Waterloo Cobol)
If I rummage through my basement I might still find some boxes of computer cards punched out in those programs.
Many of Graham's students are now big-shots at RIM (Research in Motion or the Blackberry Company, based right here in Waterloo)
http://csg.uwaterloo.ca/~jwgraham/g+m/liveslived.htm
We used the Waterloo software at MIT in fact, same era.
Sure! I'd be happy to help you solve this system of equations step-by-step.
To solve the system of equations:
1. Write the given equations in matrix form. The coefficients of the variables will be on the left side of the vertical line and the constants on the right side of the vertical line.
The first equation can be written as:
[1 1 | 7]
The second equation can be written as:
[2 -1 | 5]
2. Apply the Gaussian elimination method to transform the augmented matrix into row-echelon form.
Start by eliminating the coefficient of x in the second equation. Multiply the first equation by 2 and subtract it from the second equation:
[1 1 | 7]
[2 -1 | 5]
becomes
[1 1 | 7]
[0 -3 | -9]
3. Next, multiply the second equation by -1/3 to simplify the coefficient of y:
[1 1 | 7]
[0 1 | 3]
4. Now, to eliminate the coefficient of y in the first equation, multiply the second equation by -1 and add it to the first equation:
[1 0 | 4]
[0 1 | 3]
5. The row-echelon form indicates that x is equal to 4 and y is equal to 3.
Therefore, the solution to the system of equations is (4, 3).
Congrats! You have solved the system of equations by using the Gaussian elimination method.