The matrix A is a real symmetric 5 x 5 matrix with eigenvalues 3,7, 10, 15, and 21. The vector æ1 is an eigenvector of A with eigenvalue 3, the vector x, is an eigenvector of A with eigenvalue 7, the vector a3 is an eigenvector of A with eigenvalue 10, the vector 24 is an eigenvector of A with eigenvalue 15, and the vector æ; is an eigenvector of A with eigenvalue 21. Compute the dot products of the eigenvectors a with each other. x1. x2 = x1• 23 = x1. X4 = x2· X3 = x2 · X4 = X2 · X5 = X3 · X4 = x3 · X5 = X4 . X5 =

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