SOLUTION: I have a homework problem that I don't know how to do. I'm asked to solve the following problem; For what values of h is v3 in span {v1,v2} and for what values of h is {v1,v2,

Question 26495: I have a homework problem that I don't know how to do.
I'm asked to solve the following problem;
For what values of h is v3 in span {v1,v2} and for what values of h is {v1,v2,v3}linearly dependent?
given that

----[ 1]-----[-2]------[ 2]
v1=[-5]-v2=[10]--v3=[-9]
----[-3]-----[ 6]-------[ h]

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
I have a homework problem that I don't know how to do.
I'm asked to solve the following problem;
For what values of h is v3 in span {v1,v2} and for what values of h is {v1,v2,v3}linearly dependent?
given that
----[ 1]-----[-2]------[ 2]
v1=[-5]-v2=[10]--v3=[-9]
----[-3]-----[ 6]-------[ h]
LET US TAKE 3D SPACE WITH,I,J AND K AS UNIT VECTORS...SO
V1=1I-5J-3K
V2=-2I+10J+6K
V3=2I-9J+HK
WE FIND HERE THAT V2=-2V1...SO THEY ARE NOT INDEPENDENT...PLEASE CHECK THE NUMBERS AND COME BACK.HOWEVER ,I AM GIVING THE METHOD OF SOLUTION BELOW..
IF V3 IS IN V1 AND V2 SPAN ,THEN WE HAVE
V3=AV1+BV2=
2I-9J+HK=AI-5AJ-3AK-2BI+10BJ+6BK= I(A-2B)+J(10B-5A)+K(6B-3A)
HENCE SOLVE FOR A AND B FROM EQNS.I AND II AND SUBSTITUTE THOSE VALUES IN EQN.III TO GET H VALUE..HERE YOU WILL NOT GET THE ANSWER.
A-2B=2.......................I
10B-5A=-9....................II
6B-3A=H.......................III
THE ABOVE CASE IS FOR V1,V2,V3 TO BE DEPENDENT.
SO CHECK YOUR SECOND QUESTION AGAIN..THEY ARE INDEPENDENT OR DEPENDENT?
IF V1,V2,V3 ARE TO BE INDEPENDENT ,H SHOULD NOT BE EQUAL TO THE VALUE OBTAINED AS ABOVE.
RELATED QUESTIONS
I'm don't remember how to do my math homework. Problem is Sketch the graph of each line.... (answered by ankor@dixie-net.com)

a firework is launched from the top of a 216ft building with an initial upward velocity (answered by sroberts978,MathTherapy)

a firework is launched from the top of a 216ft building with an initial upward velocity... (answered by sroberts978,MathTherapy)

Here�s the problem: For a car renting for $15 per day plus $.10 per mile, the cost for (answered by stanbon)

Dear sir/ma'am, I have a question regarding how to solve Quad. Equations. My brother... (answered by edjones)

My homework problem: If increase the average speed of a 189 mile trip by 12mph will... (answered by Fombitz)

I have problem about probability. "You and your friend are playing on a recreational... (answered by KMST)

i have a problem with my math homework. This is the problem i got stuck i know how to do... (answered by Alan3354)

Question regarding about Quadratic Function. This is the problem: A quadratic... (answered by nerdybill)