can somebody check if this is correct:
Given two bases Xi and Yi such that Xi=aji*Yi. (1)Prove that the matrix with element aij is non singular. (2)Hence find the inverse transformation.
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?