Apply the eigenvalue method to find a general solution of the given system. Use a computer system or graphing calculator to construct a direction field and typical solution curves for the given system. x1 = 3x1 +4x21 X 2 = 6x1 - 5x2

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The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply the eigenvalue method to find a general solution of the system. x1 = 3x1 + x2 + x3, x2 = -7x15x2-X3, X3 = 7x1 + 7x2 + 3x3 What is the general solution in matrix form? x(t) =

-4 -3 Find the eigenvalues of matrix A. 1 & 2 В. -1 & 2 C. 1 & - 2 D. -1 & -2 E. None

Diagonlize the matrix if possible. the eigenvalues are as follows λ=3,1 7 4 16 2 5 8 -2 -2 -5

Find the matrix A of the quadratic form associated with the equation. 4x2 - 6xy - 4y2 + 6 = 0 A = 4 -3 P = -3 -4 Find the eigenvalues of A. (Enter your answers as a comma-separated list.) λ = 5, -5 Find an orthogonal matrix P such that PTAP is diagonal. (Enter the matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.) [1,0], [0,1]

Find the general solution of the following inhomogeneous systems. Use either eigenvector decomposi- tion or undetermined coefficients method. These problems can be solved by hand, but you can also use technology to assist you at any stage. When using technology always report on what function you use. **BHRAIBHS] -2 5 5 -2 (a) = (b) + = 2 -1 **[G]HBKH[**] 3 -2 3e + -2t cos 3t

Please help with questions 2 and 3.