Determine if the statements below are True or False. If it's True, explain why. If it's False, explain why not, or simply give an example demonstrating why it's false. A correct choice of "True" or "False" with no explanation will not receive any credit. (a) If A and B are subspaces of R3³ then AUB is a subspace of R³. Note: The notation AUB is denoting the union of A and B, i.e. AUB = { € R³ : 7 € A or 7 € B} (b) Suppose T: R³ → R³ is a linear transformation with standard matrix AȚ. If T dim(im(AT)) 3. (c) If {u, v, w} is an independent set in a subspace U, then dim(U) ≤ 3. 1 ()-(C)- 0 = 0 0 " then

-2 3 Let v₁ = V2 -3 and w = - 3 Determine if w is in the subspace of R³ generated by 4 7 10 V₁ and V2.

Please help me this question clearly, type by computer, and please explain or refer what type of method did you use??

I only need help on part (c).  I was able to figure out part (a) on my own.