Consider the matrix A - 24 -8 15 (a) Calculate the det(A − xI), where x is a variable. We call the result the characteristic polynomial of A. (b) Give the two zeros 1 and 22 of this polynomial. λ1 and 22 are called the eigenvalues of the matrix A. that Avi hivi. -13 (c) For each eigenvalue λ1, find an eigenvector vi = = (d) Construct the matrix D = (2.1 0 are eigenvectors v1 and v2. Calculate ODO 0 22 xi (*) + (8) Su # yi and the matrix Q whose columns what do you notice?

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