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new =

[ (29*y2)/5 - (7*z2)/10, 7*z2, -7*y2]

>> dif=MRA-Mprll

dif =

-0.1337 -9.7234 1.3349

>> syms y2 z2

>> eqn = new - dif ==0 ;

>> solve(eqn)

ans =

struct with fields:

y2: [0×1 sym]

z2: [0×1 sym]

John D'Errico
on 8 Sep 2020

As I explained in my comment to @Vasishta Bhargava, this is a problem with 3 equations, but only 2 unknowns. It is known as an over-determined problem. As such, it likely never has an exact solution, so solve cannot solve it.

Typically, one might use a tool like a linear regression, to find y2 and z2 that will minimize the errors in the three equations at once. I'll be lazy here and just use fminsearch.

new = @(yz) [(29*yz(1))/5 - (7*yz(2))/10, 7*yz(2), -7*yz(1)];

dif = [-0.1337 -9.7234 1.3349];

obj = @(yz) norm(new(yz) - dif);

yz = fminsearch(obj,[1 1])

yz =

-0.190698528012633 -1.38904515739705

How well did it work?

[new(yz);dif]

ans =

-0.133719852295332 -9.72331610177938 1.33488969608843

-0.1337 -9.7234 1.3349

quite well in fact.

I could also have use a direct linear regression.

[A,B] = equationsToMatrix(eqn);

double(A)\double(B)

ans =

-0.190698604595212

-1.38905731126807

So the same answer, but this time it is more precise, since fminsearch uses a tolerance.

Vasishta Bhargava
on 8 Sep 2020

Edited: Vasishta Bhargava
on 8 Sep 2020

Type

>>ans.y2

>>ans.z2

in command window to see the values

Try this code

%if true

% code

%end

syms y2 z2

new =

[ (29*y2)/5 - (7*z2)/10, 7*z2, -7*y2];

dif =

[ -0.1337 -9.7234 1.3349];

eqn = new - dif ==0 ;

A = solve(eqn,[y2,z2]); % the correct syntax

>> A.y2

>> A.z2

John D'Errico
on 8 Sep 2020

@ Waritwong Sukprasongdee:

No. You found a value of y and z only because you allowed for slight inaccuracies in your data. The values in dif

dif =

-0.1337 -9.7234 1.3349

Are not truly exact, but only 4 significant dogit approximations. Solve however, does not recognize that it can ignore the small errors made in the 4th decimal digit. So it cannot exactly solve the problem.

READ MY ANSWER.

Vasishta Bhargava
on 8 Sep 2020

@ madhan Ravi

Some of text in comment is jumbled. Sorry for inconvenience. That text is deleted

The inet connection at my place is slow. May be thats the reason. Not mathworks cloud

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