How to Simplify a matrix multiplication to get an equation

Question

I have a matrix multiplication in order to receive an equation. I have solved it, but I'm not sure of the answer. Can you guys help me out here.??

 

The first matrix is a 2×2 matrix :

                                                         cosϴ    sinϴ

                                                         5sinϴ   5cosϴ

 

The second matrix is a 2x1 matrix :

                                                          dx+Ix.tanh(x̄)
                                                          dy+Iy.tanh(ȳ)

 

The answer equals to a 2x1 matrix :          

                                                              u

                                                              w

 

The answers that I have got : 

 

u= dx.cosϴ + Ix.cosϴ.tanh(x̄)+ dy.sinϴ + Iy.sinϴ.tanh(ȳ)

 

w= -5.dx.sinϴ - 5.Ix.sinϴ.tanh(x̄) + 5.dy.cosϴ + 5.cosϴ.Iy.tanh(ȳ)

 

 

Are these answers that I got are correct,,??

I have a matrix multiplication in order to receive an equation. I have solved it, but I'm not sure of the answer. Can you guys help me out here.??

Answer 1

If the 2x2 matrix is correct, then there is a sign error in w.  The first 2 terms of w should have a positive sign.  However, if there is a typo in the 2x2 matrix, and you meant element 21 to be

 

a₂₁ = -5sinθ,

 

then w is correct.  Other than that, it looks good.  But either the sign of a₂₁ is reversed, or those first 2 terms of w have the wrong signs.  Let me know if you agree.