Let x(¹) (t) = = -3t e 4e-3t, 0 0 x (²) (t) = [_5e-31]. -5e-3t, 0 Are the vectors x(¹) (t), x(²) (t) and x(³) (t) linearly independent? choose ◆ -3t []=[]+[ [4e-3t x (³) (t) If the vectors are independent, enter zero in every answer blank since those are only the values that make the equation below true. If they are dependent, find numbers, not all zero, that make the equation below true. You should be able to explain and justify your answer. -5e-3t = + +0[ -5e- -3t .-35e-3t -5e-3t -35e-3t

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
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Question
Let
x(¹) (t) =
-3t
e
4e-3t,
0
x (²) (t) = [_5e-³]; x (³) (t)
=
-5e-3t,
Are the vectors x(¹) (t), x(²) (t) and x(³) (t) linearly
independent?
choose
◆
If the vectors are independent, enter zero in every answer
blank since those are only the values that make the equation
below true. If they are dependent, find numbers, not all zero,
that make the equation below true. You should be able to
explain and justify your answer.
0
-3t
[8] = 0[*]+[-+*
0
[4e-3t
-5e-3t
-0[
+
-5e-3t
-35e-3t
-5e-3t
-35e-3t
Transcribed Image Text:Let x(¹) (t) = -3t e 4e-3t, 0 x (²) (t) = [_5e-³]; x (³) (t) = -5e-3t, Are the vectors x(¹) (t), x(²) (t) and x(³) (t) linearly independent? choose ◆ If the vectors are independent, enter zero in every answer blank since those are only the values that make the equation below true. If they are dependent, find numbers, not all zero, that make the equation below true. You should be able to explain and justify your answer. 0 -3t [8] = 0[*]+[-+* 0 [4e-3t -5e-3t -0[ + -5e-3t -35e-3t -5e-3t -35e-3t
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