I need to know if these vectors are linearly independent or not- According to answer at least two should be but I don't know how to find out please help

{(1,-1,1) (3,1,5) (1,1,2)}

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- July 23rd 2012, 06:47 AMrohan03are these vectors linearly independent?
I need to know if these vectors are linearly independent or not- According to answer at least two should be but I don't know how to find out please help

{(1,-1,1) (3,1,5) (1,1,2)} - July 23rd 2012, 07:00 AMemakarovRe: are these vectors linearly independent?
See Wikipedia for an example.

- July 23rd 2012, 07:26 AMHallsofIvyRe: are these vectors linearly independent?
It's always good to start with the

**definitions**. A set of vectors, [tex]\{v_1, v_2, v_3, \cdot\cdot\cdot, v_n\}[/itex] are "independent" if and only if the only way we can have

is to have .

In this example, you would have

.

That is, you have the three equations:

If the only solution to those three equations is then the vectors are independent. If there are other solutions (a system of n homogeneous linear equations in n unknowns has a single unique solution, or has an infinite number of solutions) the vectors are dependent.