# : 3. Which of the following are subspaces of R°, if it is not explain briefly why not: (a) The zero vector (b) The line

: 3.
Which of the following are subspaces of R°, if it is not explain briefly why not:
(a) The zero vector
(b) The line through (1, 2, 3) and (0,0,0)
(c) The line through (1, 2, 3) and (4, 5, 6)
(d) The plane 7x + 77y + 777z = 0
(e) A sphere of radius 1 centered at (1,0,0)
(f) The yz-plane (i.e. x=0)
(g) Can a basis for R’ contain 9 vectors? Explain why or why not.
1
(h) Normalize the vector v =

(550 words)

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