Something is wrong with my Matlab

Hi, today I saw a challenge on internet, so I decided to solve it using math and Matlab to check if I was right.

It was about a 3x3 system of equations.

The equation was:

A = [x x x; x y y; y -2z]
b = [60 30 3]'

And this is what I used.

A = [1 1 1; 1 1 1; 0 1 -2]
b = [60 30 3]'

When I found out the values of x, y and z, the values were: x = 20, y = 5 and z = 1.

But, on Matlab, they showed me the values for x = 16.28, y = 20 and z = 8.5.

I used the "A\b" command and after I used the "pinv(A)*b" command.

What I did wrong? Can you help me with that?

Answer 1

[Steven Lord]

A = [x x x; x y y; y -2z]
b = [60 30 3]'

I suspect this is supposed to represent the equations 3*x = 60, x+2*y = 30, y-2*z = 3. That's not how I would have written them, but the question you're asking is about how to write them.

A = [1 1 1; 1 1 1; 0 1 -2]
b = [60 30 3]'

Those two matrices represent the equations x+y+z = 60, x+y+z = 30, y-2*z = 3. Those don't match the equations from the original problem, and the first two equations aren't consistent. How can the sum of x, y, and z simultaneously be equal to 60 and equal to 30?

The first element of the first row of your A should be the coefficient of the first variable in the first equation.

The second element of the first row of your A should be the coefficient of the second variable in the first equation.

The first element of the third row of your A should be the coefficient of the first variable in the third equation.

Can you translate the original equations into A using this pattern?

[Juan Pablo Arrieta]

I did it and I solve it.

The only thing I needed to do was replace A like this:

A = [3 0 0; 1 2 0; 0 1 -2]

Because "x + x + x" is "3*x" and the rest of the coefficients were 0.

The other equation "x + y + y" is "x + 2*y" and the other coefficient is 0.

The last one its okay.

The results were what I wrote at the beginning.

x = 20
y = 5
z = 1

Thank you very much! You helped me a lot!

And I apologize if my english isn't as good as a native speaker.

[Steven Lord]

You're welcome! And your English was good, I could understand what you said without a problem.