Consider the set of all 2×2 matrices. This set is a vector space, which we will call X (yes, matrices can be vectors). If M is an element of this vector space, define the transformation Consider the following basis set for the vector space X.i. Find the matrix representation of the transformation relative to the basis set (for both domain and range) (using Eq. (6.6)).ii. Verify the operation of the matrix representation from part i. on the element of X given below. (Verify that the matrix multiplication produces the same result as the transformation.)iii. Find the eigenvalues and eigenvectors of the transformation. You do not need to use the matrix representation that you found in part i. You can find the eigenvalues and eigenvectors directly from the definition of the transformation. Your eigenvectors should be 2×2 matrices (elements of the vector space X). This does not require much computation. Use the definition of eigenvector in Eq. (6.46).
Consider the set of all 2×2 matrices. This set is a vector space, which we will call X (yes,…
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