# Linear dependence for dummies

I don't have a background in math; I do have a basic understanding of linear algebra though. I am trying to understand the next part from "Deep learning" book: I don't understand what they are explaining in that paragraph. I played around with the formula and I got:

$$\alpha=0, \ \ \ z=y$$

$$\alpha=1, \ \ \ z=x$$

$$\alpha=2,\ \ \ z=2x-y$$

$$\alpha=-1,\ \ \ z=-x+2y$$

$$\alpha=-2, \ \ \ z=-2x+3y$$

I don't know where this is going... Also per the paragraph explanation, I am expecting a formula that includes b.

Unfortunately, given my lack of math I am only comfortable with graphical explanations or real life examples.

• they are explaining that if there are two (i.e., more than one) solutions, then there are infinitely many solutions (which can be generated from the two solutions $\mathbb x$ and $\mathbb y$) – J. W. Tanner Dec 3 at 0:31
• I assume (2.11) is something like "$Ax = b$"? – Eric Towers Dec 3 at 0:31
• If $Ax=b$ and $Ay=b$ then $$Az=A(\alpha x+(1-\alpha)y)=\alpha Ax+(1-\alpha)Ay=\alpha b+(1-\alpha)b=b.$$ – A.Γ. Dec 3 at 0:32