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
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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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 R³ then AUB is a subspace of R³. Note: The notation AUB is denoting the
union of A and B, i.e. AUB = { € R³ : ≈ € A or x € B}
1
0
IT()-()
0 =
0
0
(b) Suppose T: R³ → R³ is a linear transformation with standard matrix AT. If T
dim(im(AT)) # 3.
(c) If {u, v, w} is an independent set in a subspace U, then dim(U) ≤ 3.
"
then
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