Question

a) are they linearly dependent? (-3,0,4),(5,-1,2),1,1,3)
b)show that 3 vectors in R3 form a linearly dependent set in R4 v1=(o,3,1,-1); v2=(6,0,5,1);v3= (4,-7,1,3)

Answer 1

I confused don't know when we use column/row to express the vectors in matrix to consider they are linearly dependent or not. Anyone explain me, please. just that stuff. the leftover is mine. I know how to prove it. Please.

Answer 2

\[\left[\begin{matrix}-3 & 0 &4 \\ 5 & -1 & 2\\1 &1 & 3\end{matrix}\right]or \left[\begin{matrix}-3 & 5 &1 \\ 0 & -1 & 1\\4 & 2 & 3\end{matrix}\right]\]

Answer 3

which one is the right matrix for me to consider they are linear dependent or not?

Answer 4

@Hoa how can u unified 3 row vectors or row matrices in one matrix?

Answer 5

it's the process to figure out whether they are linear dependent or independent. is it not right?

Answer 6

no its not the process
the process for determining linear dependence and independence of vectors is as follow :
Vectors ( or matrices ) X1 , X2 , X3 ,... Xn are said to be dependent
(1) all the vectors ( row or column ) are of the same order
(2) n scalars a1 , a2 , a3, ..an(not all zero) exist such that
a1X1 + a2X2 + a3X3+..+anXn = 0
otherwise they are linearly independent

Answer 7

yes, the same idea, the same thing. I studied that information too. put your equation into the linear combination, you get exactly what i have. x1 = <-3,0,4> ...something like that. and you have the same matrix I have

Answer 8

but u need to solve for the scalars in order to see whether they are linear independent or dependent

Answer 9

you have 3 equations to solve for your a1,a2,a3 that means
-3a1 +5a2+1a3=0 and then 0 a1-1a2+1a3 =0, and then 4a1 +2a2+3a3 =0 and you have exactly my matrix

Answer 10

I think you confused. the matrix I set up is to solve for your scalar. if you have any scalar satisfy that matrix it means they are linear dependent. if not they are independent

Answer 11

yeah i know u will get the second one matrix

Answer 12

thanks

Answer 13

so row vectors are linearly dependent

Answer 14

I don't solve it yet. just make sure about the matrix first, the leftover is easy

Answer 15

u will get the second one matrix that for sure :-P

Answer 16

i confused, because sometimes, my pro uses the first matrix, to me, the second one makes more sense than the first one.

Answer 17

How can first matrix be used? I m confused too

Answer 18

wait, i send email to ask my pro already. if i have his answer, i will let you know