Vector space question

[cotfw]

I don't quite understand this. I've attached a photo of the question in the textbook, and in the question, at one point it says "this yields the set of linear equations..." but I have no clue how it yields that set. It's "example 2"

Do you know?

 

[stapel]

Sorry, but I'm having trouble reading the fuzzy sideways graphic. Please reply with the typed-out text (or a greatly clarified graphic).

When you reply, please include a clear listing of your efforts in working out the example, so we can see where you're getting something other than what the book indicates. Thank you!

 

[Steven G]

I don't quite understand this. I've attached a photo of the question in the textbook, and in the question, at one point it says "this yields the set of linear equations..." but I have no clue how it yields that set. It's "example 2"

Do you know?

You are studying linear algebra and can't understand this?

Here are some examples

if 3x^2 + 2 x -5 = ax^2 + bx + c then a=3, b=2 and c=-5

if 4x^4-3x^2-11 = ax^4 + bx^3 + cx^2 + dx + e then a =4, b=0, c= -3, d=0 and e= -11

just equate the coefficients of like terms. Have enough mathematical maturity to know that you can add 0 to any equation and that 0x^n equals 0 for any non negative n.