Verify that the vector X is a solution of the given homogeneous system. X' = (−1 1 1/25 -1)X; X = (−1 5)e−6t/5
For X = (−1 5)e−6t/5, one has
Since the above expressions, X = (−1 5)e−6t/5 is a solution of the given system.
The given vectors are solutions of a system X' = AX. Determine whether the vectors form a fundamental set on the interval (-co, o).
X1 = (1 -2 4) + t(1 2 2), X2 = (1 -2 4), X3 = (2 -4 8) + t(4 4 8)
A. Yes, since the set X,, X,, X3 is linearly independent for -o B. Yes, since the set X,, X2, X3 is linearly dependent for -t C. No, since the set X,, X2, X3 is linearly independent for -co t<.
D. No, since the set X, X2, X, is linearly dependent for -oo