1. (3 point) Let vā =
$\begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}$, V2 =
$\begin{bmatrix} 1 \\ 3 \\ 1 \end{bmatrix}$, V3 =
$\begin{bmatrix} 2 \\ 6 \\ 2 \end{bmatrix}$, V4 =
$\begin{bmatrix} 3 \\ 9 \\ -1 \end{bmatrix}$, V5 =
$\begin{bmatrix} 0 \\ 0 \\ -4 \end{bmatrix}$, and let W = span{V1, V2, V3, V4, V5}.
a) Find a subset of the vectors {V1, V2, V3, V4, V5} that form a basis for W.
b) Find dim(W) =
c) Which of the following is a geometric description of W? Circle the correct answer.
i) W is a point in R2.
iv) W is a line in R2.
vii) W is a plane in R2.
ii) W is a point in RĀ³.
iii) W is a point in R4.
vi) W is a line in R4.
ix) W is a plane in R4.
v) W is a line in RĀ³.
viii) W is a plane in RĀ³.
x) W is a hyperplane in RĀ². xi) W is a hyperplane in RĀ³. xii) W is a hyperplane in R4.
