Recall what it means to be linearly dependent:

A subset

*S* of vector space

*V* is called

*linearly dependent* if there exist a finite number of distinct vectors

**v**1,

**v**2, ...,

**v***n* in

*S* and scalars

*a*1,

*a*2, ...,

*a**n*, not all zero, such that

Note that the zero on the right is the

zero vector, not the number zero.

Here your distinct vectors are x, y, z as opposed to v_1, V_2,...,v_n. since you are considering only 3 vectors, you can prove they are linearly independent by showing there are distinct constants (that's why it says not all zero) that you can multiply each vector by and get the zero vector. this proof simply chose those three constants to be 1, -k, and 0.

(1)y + (-k)x + (0)z = 0

You get all the other steps right?