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Consider the vector space of functions of the form One basis set for this vector space is…

Consider the vector space of functions of the form One basis set for this vector space is…

Consider the vector space of functions of the form  One basis set for this vector space is  Consider the differentiation transformation i. Find the matrix of the transformation  relative to the basis set V, using Eq. (6.6).ii. Verify the operation of the matrix on the function iii. Find the eigenvalues and eigenvectors of the transformation. Show the eigenvectors as columns of numbers (with respect to the basis set V) and as functions of t.iv. Find the matrix of the transformation relative to the eigenvectors as basis vectors.