Advanced Math/transposes

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Question
I am having difficulty doing this. I know most of the question involve the transpose but i do not know what to do Thanks for any help

Solve for the matrix X in the following equations.
(a) (B^-1X)^TC^-1 = (CB)^-1

(b) [2 1]        [4 1 0]   [0 0]
   [1 4]X^T = -4[2 2 5] + [0 3]X^T

Answer
a) (B^-1X)^TC^-1 = X^T(B^-1)^T(CB)^-1 = B^-1C^-1

mult by C on right then mult by B^T

X^T(B^-1^T)B^T = X^T(B^-1B)^T = X^T = B^-1B^T

(X^T)^T = X = B(B^-1)T

b) Note first of all that the matrix X^T must be a 3x2 matrix in order to match the given matrices. Write X^T as

x11  x21  x31
x21  x22  x23

and carry out the matrix multiplication. You'll get 6 equations in 6 unknowns which you can solve for the elements of X.

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randy patton

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college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

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26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

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J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

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