- #1
HAMJOOP
- 32
- 0
Given two vectors
x(t) = (e^t te^t)^T
y(t) = (1 t)^T
a) Show that x and y are linearly dependent at each point in the interval [0, 1]
b) Show that x and y are linearly independent on [0, 1]
I compute det([x y]) = 0, so they are linearly dependent
how about part b. Isn't a) and b) are contradictory
The above problem comes from Elementary Differential Equations and Boundary Value Problems 9th ed.
Another question
given two vectors depends on t, v and w each has two components
det([v w]) = 0 at some points only
Can I say v and w are linearly dependent at those points ??
x(t) = (e^t te^t)^T
y(t) = (1 t)^T
a) Show that x and y are linearly dependent at each point in the interval [0, 1]
b) Show that x and y are linearly independent on [0, 1]
I compute det([x y]) = 0, so they are linearly dependent
how about part b. Isn't a) and b) are contradictory
The above problem comes from Elementary Differential Equations and Boundary Value Problems 9th ed.
Another question
given two vectors depends on t, v and w each has two components
det([v w]) = 0 at some points only
Can I say v and w are linearly dependent at those points ??