How Can I solve this equations system?

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Mehmet 2014-2-25

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关闭： MATLAB Answer Bot 2021-8-20

K.a+M.b=L.b
P.a+ Q .b=R.a

I have the equations above and I am trying to find a and b. All capital letters are constants. How can I solve this problem in Matlab?

Thanks

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Answer 1

Walter Roberson 2014-2-25

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Do the "." represent multiplication? Are the elements all scalars or are they matrices?

If everything is scalar and "." represents ordinary multiplication, then the solution is a = 0, b = 0.

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Mehmet 2014-2-26

编辑：Mehmet 2014-2-26

Actually I should tell you my problem with a different way;

My equations are; (Ty25=Ty and Tx25=Tx so I am trying to find alpha and beta values)

Ty25 =

(551666622438673794225934829796875*beta)/1045347431181122959759486794030391945592832

Tx25 =

(551666622438673794225934829796875*alpha)/1045347431181122959759486794030391945592832

Ty =

(8563063365494341*cos(alpha)^2*((log(sin(alpha)*sin(beta) - cos(alpha) - 225)*(cos(alpha) + 225))/(1000000*cos(alpha)*(cos(alpha)^2 - 1)*(cos(beta)^2 - 1)) - (log(200*sin(alpha)*sin(beta) - cos(alpha) - 225)*(cos(alpha) + 225))/(1000000*cos(alpha)*(cos(alpha)^2 - 1)*(cos(beta)^2 - 1)) + (log(8*sin(alpha)*sin(beta) - 8*cos(alpha) - 9)*(8*cos(alpha) + 9))/(40000*cos(alpha)*(cos(alpha)^2 - 1)*(cos(beta)^2 - 1)) - (log((sin(alpha)*sin(beta))/25 - 8*cos(alpha) - 9)*(8*cos(alpha) + 9))/(40000*cos(alpha)*(cos(alpha)^2 - 1)*(cos(beta)^2 - 1))))/(4835703278458516698824704*(pi - 2*alpha)^2) - (8563063365494341*cos(alpha)^2*((log(- cos(alpha) - sin(alpha)*sin(beta) - 225)*(cos(alpha) + 225))/(1000000*cos(alpha)*(cos(alpha)^2 - 1)*(cos(beta)^2 - 1)) - (log(- cos(alpha) - 200*sin(alpha)*sin(beta) - 225)*(cos(alpha) + 225))/(1000000*cos(alpha)*(cos(alpha)^2 - 1)*(cos(beta)^2 - 1)) + (log(- 8*cos(alpha) - 8*sin(alpha)*sin(beta) - 9)*(8*cos(alpha) + 9))/(40000*cos(alpha)*(cos(alpha)^2 - 1)*(cos(beta)^2 - 1)) - (log(- 8*cos(alpha) - (sin(alpha)*sin(beta))/25 - 9)*(8*cos(alpha) + 9))/(40000*cos(alpha)*(cos(alpha)^2 - 1)*(cos(beta)^2 - 1))))/(4835703278458516698824704*(pi - 2*alpha)^2) - (8563063365494341*(1791/(1000000*cos(beta)^2*(8*cos(beta) - 9)) - 1791/(1000000*cos(beta)^2*(cos(beta)/25 - 9)) - (199*log(8*cos(beta) - 9))/(1000000*cos(beta)^2) + (199*log(cos(beta)/25 - 9))/(1000000*cos(beta)^2)))/(19342813113834066795298816*(sin(beta)^2/(cos(alpha)^2*cos(beta)^2) + 1)*(pi/2 - atan(sin(beta)/(cos(alpha)*cos(beta))))^2) - (8563063365494341*(1791/(1000000*cos(beta)^2*(8*cos(beta) + 9)) - 1791/(1000000*cos(beta)^2*(cos(beta)/25 + 9)) + (199*log(- 8*cos(beta) - 9))/(1000000*cos(beta)^2) - (199*log(- cos(beta)/25 - 9))/(1000000*cos(beta)^2)))/(19342813113834066795298816*(sin(beta)^2/(cos(alpha)^2*cos(beta)^2) + 1)*(pi/2 - atan(sin(beta)/(cos(alpha)*cos(beta))))^2)

Tx =

68160280339725220986141/(967140655691703339764940800000000*(sin(beta)^2/(cos(alpha)^2*cos(beta)^2) + 1)*(pi/2 - atan(sin(beta)/(cos(alpha)*cos(beta))))^2*(8*cos(beta)^2 - 1809*cos(beta) + 2025)) - (8563063365494341*cos(alpha)^2*((log(- cos(alpha) - sin(alpha)*sin(beta) - 225)*(cos(alpha) + 225))/(1000000*cos(alpha)*(cos(alpha)^2 - 1)*(cos(beta)^2 - 1)) - (log(- cos(alpha) - 200*sin(alpha)*sin(beta) - 225)*(cos(alpha) + 225))/(1000000*cos(alpha)*(cos(alpha)^2 - 1)*(cos(beta)^2 - 1)) + (log(- 8*cos(alpha) - 8*sin(alpha)*sin(beta) - 9)*(8*cos(alpha) + 9))/(40000*cos(alpha)*(cos(alpha)^2 - 1)*(cos(beta)^2 - 1)) - (log(- 8*cos(alpha) - (sin(alpha)*sin(beta))/25 - 9)*(8*cos(alpha) + 9))/(40000*cos(alpha)*(cos(alpha)^2 - 1)*(cos(beta)^2 - 1))))/(4835703278458516698824704*(pi - 2*alpha)^2) - (8563063365494341*(1791/(1000000*cos(beta)^2*(8*cos(beta) + 9)) - 1791/(1000000*cos(beta)^2*(cos(beta)/25 + 9)) + (199*log(- 8*cos(beta) - 9))/(1000000*cos(beta)^2) - (199*log(- cos(beta)/25 - 9))/(1000000*cos(beta)^2)))/(19342813113834066795298816*(sin(beta)^2/(cos(alpha)^2*cos(beta)^2) + 1)*(pi/2 - atan(sin(beta)/(cos(alpha)*cos(beta))))^2) + (8563063365494341*cos(alpha)^2*((log(8*sin(alpha)*sin(beta) - 8*cos(alpha) - 9)*(8*sin(alpha)*sin(beta) - 9))/(40000*cos(alpha)^2*sin(alpha)*sin(beta)) - (log(8*sin(alpha)*sin(beta) - cos(alpha)/25 - 9)*(8*sin(alpha)*sin(beta) - 9))/(40000*cos(alpha)^2*sin(alpha)*sin(beta)) + (log(sin(alpha)*sin(beta) - cos(alpha) - 225)*(sin(alpha)*sin(beta) - 225))/(1000000*cos(alpha)^2*sin(alpha)*sin(beta)) - (log(sin(alpha)*sin(beta) - 200*cos(alpha) - 225)*(sin(alpha)*sin(beta) - 225))/(1000000*cos(alpha)^2*sin(alpha)*sin(beta))))/(4835703278458516698824704*(pi - 2*alpha)^2)

Walter Roberson 2014-2-27

I ran it through Maple and did some testing. You aren't going to be able to get a symbolic solution, I don't think.

You have a difficulty in the equations. Look carefully at the log() terms. One of them is log(8*cos(beta) - 9). For all real beta, 8*cos(beta)-9 is negative, ranging from -17 to -1. Thus you are introducing a complex term. Getting rid of that requires precise cancellation of all of the complex terms in the equation, which is pretty tricky to achieve.

Now if the alpha and beta are permitted to be complex then getting a solution numerically would be easier.

Mehmet 2014-2-27