(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let {X, Y, Z} be linearly independent in Rn. If {X, Y, Z, W} is linearly dependent, show that W [tex]\epsilon[/tex] span{X, Y, Z}. NB: You must SHOW this.

2. Relevant equations

3. The attempt at a solution

For W to belong to the span of {X,Y,Z}, W = aX + bY + cZ where a, b, c are some real numbers. Since {X,Y,Z,W} is linearly dependent, one of the four vectors can be shown as a linear combination of the other three, ie. W = aX + bY + cZ, where a, b, c are some real numbers.

On my assignment, I have the previous statement, and I've also represented X, Y, Z, and W with {x_{1}, x_{2}, x_{...}, x_{n}}, etc. I've taken these equations and multiplied the real numbers in.

I know what I'm trying to say here, but I don't exactly know how to say it, if you know what I mean. Is my explanation enough? Does it SHOW that W belongs to the span of {X, Y, Z}?

Thanks,

Connor Bode

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Linear independence

**Physics Forums | Science Articles, Homework Help, Discussion**