Exercise 7
\begin{bmatrix} 2 \\ 4 \\ 3 \\ 2 \\ 4 \\ 5 \end{bmatrix}, v = \begin{bmatrix} 2 \\ 4 \\ 6 \\ 1 \\ 7 \\ 3 \\ 5 \end{bmatrix}, w = \begin{bmatrix} 2 \\ 4 \\ 0 \\ 5 \\ 2 \\ 3 \\ 5 \end{bmatrix}, and z = \begin{bmatrix} 2 \\ 4 \\ 3 \\ 7 \\ 5 \\ 3 \\ 5 \end{bmatrix}.
Let u =
a. Are the sets \{u, v\}, \{u, w\}, \{u, z\}, \{v, w\}, \{v, z\}, \{w, z\} each linearly
independent? Why or why not?
b. Does the answer to Part (a) imply that \{u, v, w, z\} is linearly indepen-
dent?
c. To determine if \{u, v, w, z\} is linearly dependent, is it wise to check if,
say, w is a linear combination of u, v, and z?
d. Is \{u, v, w, z\} linearly dependent?