The general solution of the linear system X' = AX is given. -105t 30 A =...

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The general solution of the linear system X' = AX is given. -105t 30 A = X(t) = c, el+ 6 (a) In this case discuss the nature of the solution in a neighborhood of (0, 0). O If X(0) = X, lies on the line y = -x, then X(t) approaches (0, 0) along this line. Otherwise X(t) approaches (0, 0) from the direction determined by y = -3x. O If X(0) = X, lies on the line y = -3x, then X(t) approaches (0, 0) along this line. Otherwise X(t) approaches (0, 0) from the direction determined by y = -x. O If X(0) = X, lies on the line y = -x, then X(t) becomes unbounded along this line. Otherwise X(t) becomes unbounded and y = -3x serves as an asymptote. O If X(0) = x, lies on the line y = -3x, then X(t) becomes unbounded along this line. Otherwise X(t) becomes unbounded and y = -x serves as an asymptote. O All solutions spiral toward (0, 0). (b) With the aid of a calculator or a CAS, graph the solution that satisfies X(0) = (1, 1). y 2 (1, 1) (1, 1) (1, 1) -6 -4 -2 2 4 6. -- -4 -2 2 4 6. -2 -1 1 2 The general solution of the linear system X' = AX is given. -105t 30 A = X(t) = c, el+ 6 (a) In this case discuss the nature of the solution in a neighborhood of (0, 0). O If X(0) = X, lies on the line y = -x, then X(t) approaches (0, 0) along this line. Otherwise X(t) approaches (0, 0) from the direction determined by y = -3x. O If X(0) = X, lies on the line y = -3x, then X(t) approaches (0, 0) along this line. Otherwise X(t) approaches (0, 0) from the direction determined by y = -x. O If X(0) = X, lies on the line y = -x, then X(t) becomes unbounded along this line. Otherwise X(t) becomes unbounded and y = -3x serves as an asymptote. O If X(0) = x, lies on the line y = -3x, then X(t) becomes unbounded along this line. Otherwise X(t) becomes unbounded and y = -x serves as an asymptote. O All solutions spiral toward (0, 0). (b) With the aid of a calculator or a CAS, graph the solution that satisfies X(0) = (1, 1). y 2 (1, 1) (1, 1) (1, 1) -6 -4 -2 2 4 6. -- -4 -2 2 4 6. -2 -1 1 2