In Exercises 7-12, describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given matrix. 7. O 3-3 7 1 -4 5 3 -9 6 3-2 -1 8. 10. 2 -2 -9 1 5 2-6 3 6 0-4 0-8
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- In Exercises 17–22, determine which sets of vectors are orthonormal. If a set is only orthogonal, normalize the vectors to produce an orthonormal set.In Exercises 7–22, determine the eigenvalues and eigenvectors if the eigenvalues are real (or use results from exercises from Section 4.2. if you have covered those exercises). Also classify the system (state whether stable or unstable node, stable or unstable spiral, center, saddle point) and in all cases sketch the phase plane of the linear system. (As a hint, problems with * have complex eigenvalues.) When checking your answers with those in the back of the book, keep in mind that any nonzero multiple of the given eigenvector may be used. CORRECT ANSWER IS GIVEN. PLS SHOW STEP BY STEP HOW TO GET THERELet Q be a 3 × 3 orthogonal matrix whose determinantis equal to 1. In the case that the eigenvalues λ2 and λ3 are complex, what are the possible values for λ1? Explain.
- Suppose that a surface contains a straight line. Explain why, for any point in this line, the second fundamental form must have a 0 eigenvalue.If ldet(A)I > 1, prove that the powers An cannot stay bounded. But if ldet(A)I :S 1, show that some entries of An might still grow large. Eigenvalues will give the right test for stability, determinants tell us only one number.Describe all solutions of Ax=0in parametric vector form, where A is row equivalent to the given matrix.
- Prove that the two solution functions in Attached Theorem 4 are linearly independent.The Hamiltonian operator of a system is H=-(d2f/dx2) +x2 . Show that Nx exp (-x2/2) is an eigenfunction of H and determine the eigenvalue. Also evaluate N by normalization of the function.In Exercises 7–12, describe all solutions of in parametric vector form, where is row equivalent to the given matrix.