How to solve a unknown variables in matrix multipication using matlab?

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Ravikiran Mundewadi 2015-5-25

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https://ww2.mathworks.cn/matlabcentral/answers/218524-how-to-solve-a-unknown-variables-in-matrix-multipication-using-matlab

回答： Walter Roberson 2015-5-25

Here i am writing a Matrix say its 6x6

Y-KY*=F

Here Y=[y1 y2 y3 y4 y5 y6] , F=[six Known Values], K=[6x6 known values] Y*=[six unknown values with nonlinear combinations]

Y and Y* are unknown variables.

Here we have to find the Y1 y2 y3 y4 y5 y6

How we have to solve this using Matlab

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Answer 1

Walter Roberson 2015-5-25

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在 MATLAB Online 中打开

Under the assumption that Y and F are column vectors, then the sizes work out. However, there would be an infinite number of solutions. You are trying to solve 6 equations in 12 unknowns.

If the point is to find this symbolically, in Y* then

Y-K*Ystar=F

so

Y = F + K*Ystar

and you might as well leave it in that form. If you really need it written out, it would be

Y = [F(1, 1) + K(1, 1) * Ystar(1, 1) + K(1, 2) * Ystar(2, 1) + K(1, 3) * Ystar(3, 1) + K(1, 4) * Ystar(4, 1) + K(1, 5) * Ystar(5, 1) + K(1, 6) * Ystar(6, 1);
     F(2, 1) + K(2, 1) * Ystar(1, 1) + K(2, 2) * Ystar(2, 1) + K(2, 3) * Ystar(3, 1) + K(2, 4) * Ystar(4, 1) + K(2, 5) * Ystar(5, 1) + K(2, 6) * Ystar(6, 1);
     F(3, 1) + K(3, 1) * Ystar(1, 1) + K(3, 2) * Ystar(2, 1) + K(3, 3) * Ystar(3, 1) + K(3, 4) * Ystar(4, 1) + K(3, 5) * Ystar(5, 1) + K(3, 6) * Ystar(6, 1);
     F(4, 1) + K(4, 1) * Ystar(1, 1) + K(4, 2) * Ystar(2, 1) + K(4, 3) * Ystar(3, 1) + K(4, 4) * Ystar(4, 1) + K(4, 5) * Ystar(5, 1) + K(4, 6) * Ystar(6, 1);
     F(5, 1) + K(5, 1) * Ystar(1, 1) + K(5, 2) * Ystar(2, 1) + K(5, 3) * Ystar(3, 1) + K(5, 4) * Ystar(4, 1) + K(5, 5) * Ystar(5, 1) + K(5, 6) * Ystar(6, 1);
     F(6, 1) + K(6, 1) * Ystar(1, 1) + K(6, 2) * Ystar(2, 1) + K(6, 3) * Ystar(3, 1) + K(6, 4) * Ystar(4, 1) + K(6, 5) * Ystar(5, 1) + K(6, 6) * Ystar(6, 1)];