determine if the following pair of vectors is linearly dependent or linearly independent. show all work (3,5,6) (6,4,11) (-3,-5,6). this is vectorsDO IT THIS WAY NOT THE MATRIX OTHER WAYstart by making the equation like (-3,-5,6)=a (3,5,6)+ b(6,4,11) Ex: Are the vectors (3,-1,0), (0,2,1), and (0,0,2) nearly dependent?Let a and b be scalars.ŵ = a + b(0,0,2)= a(3,-1,0)+b(0,21)0 = 300NatsCheck in the third.LSRS0-9+zb-O+2(2)O= a + zb @ +2= bwe see b= 2 and a-- 4.. LS&RS.: the vectorsare NOTlinearly dependent.

Ex: Are the vectors (3,-1,0), (0,2,1), and (0,0,2) nearly dependent? Let a and b be scalars. ŵ = a + b (0,0,2)= a(3,-1,0)+b(0,21) 0 = 30 0 Nats Check in the third. LS RS 0 -9+zb -O+2(2) O= a + zb @ + 2= b we see b= 2 and a- - 4 .. LS&RS .: the vectors are NOT linearly dependent.

Ex: Are the vectors (3,-1,0), (0,2,1), and (0,0,2) nearly dependent? Let a and b be scalars. ŵ = a + b (0,0,2)= a(3,-1,0)+b(0,21) 0 = 30 0 Nats Check in the third. LS RS 0 -9+zb -O+2(2) O= a + zb @ + 2= b we see b= 2 and a- - 4 .. LS&RS .: the vectors are NOT linearly dependent.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.1: The Geometry And Algebra Of Vectors

Problem 4EQ

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Question

determine if the following pair of vectors is linearly dependent or linearly independent. show all work (3,5,6) (6,4,11) (-3,-5,6). this is vectors

DO IT THIS WAY NOT THE MATRIX OTHER WAY

start by making the equation like (-3,-5,6)=a (3,5,6)+ b(6,4,11)

Ex: Are the vectors (3,-1,0), (0,2,1), and (0,0,2) nearly dependent?
Let a and b be scalars.
ŵ = a + b
(0,0,2)= a(3,-1,0)+b(0,21)
0 = 30
0
Nats
Check in the third.
LS
RS
0
-9+zb
-O+2(2)
O= a + zb @ +
2= b
we see b= 2 and a-
- 4
.. LS&RS
.: the vectors
are NOT
linearly dependent.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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