2x2 matrix elimination / substitution

[martijnh]

Homework Statement

I'm following an online course on linear algebra where matrix elimination was explained. They showed this for a 3x3 matrix, I wanted to test this with a 2x2 matrix but somehow managed to do something wrong..

I have two equations with 2 unknowns:
2x - y = 0
-x + 2y = 3

which coefficients should translate into this matrix:

[ 2  -1]
[-1   2]

2. The attempt at a solution
I eliminated the x coefficient in the second row by multiplying the first row .5 times and substracting that from the second. This results in:

[2  -1  ]
[0   2,5]

When I substitute back into the original equations I get
2.5y = 3 => y = 1.25
2x - y = 0 => 2x - 1.25 = 0 => x= 0.625

But this isn't correct for the second equation (which x component was eliminated). Where did it go wrong?

Thanks,

Martijn

 

[Mark44]

Homework Statement

I'm following an online course on linear algebra where matrix elimination was explained. They showed this for a 3x3 matrix, I wanted to test this with a 2x2 matrix but somehow managed to do something wrong..

I have two equations with 2 unknowns:
2x - y = 0
-x + 2y = 3

which coefficients should translate into this matrix:

[ 2  -1]
[-1   2]

2. The attempt at a solution
I eliminated the x coefficient in the second row by multiplying the first row .5 times and substracting that from the second. This results in:

[2  -1  ]
[0   2,5]

You have two mistakes. You need to add 1/2 times the first row to the second row. That results in the second row being [0 3/2]

When I substitute back into the original equations I get
2.5y = 3 => y = 1.25
2x - y = 0 => 2x - 1.25 = 0 => x= 0.625

But this isn't correct for the second equation (which x component was eliminated). Where did it go wrong?

Thanks,

Martijn

 

[martijnh]

Doh *slaps forehead*

Thanks!

 

[Mark44]

Doh *slaps forehead*

Thanks!

Yes, that's the correct response.