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Consider the transformation A created by projecting a vector x onto the line shown in Figure…

Consider the transformation A created by projecting a vector x onto the line shown in Figure…

Consider the transformation A created by projecting a vector x onto the line shown in Figure E6.3. An example of the transformation is shown in the figure.i. Using Eq. (6.6), find the matrix representation of this transformation relative to the standard basis set ii. Using your answer to part i, find the matrix representation of this transformation relative to the basis set  shown in Figure E6.3. iii. What are the eigenvalues and eigenvectors of this transformation? Sketch the eigenvectors and their transformations.