CHECK POINT 1 Write ⊆ or ⊆ in each blank to form a true statement: a. A = { 1 , 3 , 5 , 6 , 9 , 11 } B = { 1 , 3 , 5 , 7 } A _ _ _ B b. A = { x | x is a letter in the word r o o f } B = { y | y is a letter in the word p r o o f } A _ _ _ B c. A = { x | x is a day of the week } B = { Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday } A _ _ _ B
CHECK POINT 1 Write ⊆ or ⊆ in each blank to form a true statement: a. A = { 1 , 3 , 5 , 6 , 9 , 11 } B = { 1 , 3 , 5 , 7 } A _ _ _ B b. A = { x | x is a letter in the word r o o f } B = { y | y is a letter in the word p r o o f } A _ _ _ B c. A = { x | x is a day of the week } B = { Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday } A _ _ _ B
Solution Summary: The author explains that the given statement is true for Asubseteq B.
[25 points] Given the vector let v = ER² and the collection of vectors
ε =
E-{)·()}-{☹) (9)}
= {(A)·(9)}·
B: =
and C =
· {(6)·(})}·
answer the following question.
(a)
(b)
(c)
(d)
(e)
verify
Verify is a basis for R² and find the coordinate [] of under ε.
Verify B is a basis for R2 and find the coordinate []B of ʊ
Verify C is a basis for R2 and find the coordinate []c of
under ε.
under ε.
Find the change-of-basis matrix [I]+B from basis B to basis ε, and
EE+BUB
Find the change-of-basis matrix [I]B+ε from basis Ɛ to basis B, and
verify [U]B= [] B+EVE
Explain the following terms |
(a) linear span
(b) dimension of vector space
(c) linearly independent
(d) linearly dependent
(e) rank of matrix A
3.
Let
u = 3/5
√ =
and =
-4/5
-()
Define V span{ū, }.
(a)
(b)
(c)
Show that {u, } is orthonormal and forms a basis for V.
Explicitly compute Projy w.
Explicitly give a non-zero vector in V+.
Chapter 2 Solutions
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