Question

1.Show that the set w = {(a1, az, az )ER: a + 2a2 – 3az =0} is a sub-space of
V.​

Answer 1

Answer:

Proof: By definition, F is closed under addition, so write a + b := c ∈ F. Then we have,

c(x + y) = cx + cy

by VS7. But now,

(a + b)x + (a + b)y = ax + bx + ay + by

by VS8. Finally, this is ax + ay + bx + by by VS1.