Hi,

can somebody check if this is correct:

Problem:

Given two bases X_{i}and Y_{i}such that Xi=a_{ji}*Y_{i}. (1)Prove that the matrix with element a_{ij}is non singular. (2)Hence find the inverse transformation.

Solution (1)

X=A*Y

If X and Y are bases, then Vectors (x1, x2,...,xn) and (y1,y2,...yn) are linear independent. So det(X) and det(Y)≠0.

det(X)=det(AY)=det(A)*det(Y)≠0 . If det(X), det(Y)≠0 then det(A)≠0.

Conclusion: Matrix A is non singular.

Can somebody give me a hint how to find inverse transormation?

Thanks