(8) (Section 5.1 # 5) In this problem you are W is a subspace of V and explain why V R3 given a vector V and a subset W. Decide whether or not R3 a1, a2 E R} {(1,a1,a2)) W

Linear algebra : please correctly and handwritten

How do I verify that Problem #8 is true? I think that is what it is asking for. Also, this question and many other questions in this section are very much conceptual. Although, the math can be used to verify if each question is true. This specific problem is from a linear algebra textbook called  Linear Algebra w/ Applications and the author is by Jeffrey Holt. Right now, I'm in Section 7.1, which consists of what makes a vector space a vector space. Ironically, the author mentioned something new with an R raised to a matrix, as well as a P raised to a number.  Nonetheless, I am most certainly not sure of how to answer the problem, but here are some pictures.