3. Let V=R3 and let B = (b1, b2, b3), where b₁ = ]. b2 = b3 (a) Prove B is a basis of V over R. (b) For u = 2 find the column vector [u]B. 3 a1 (c) For v = 02 find a formula for the column vector [v]B in terms of a1, a2, a3. аз () 4. Let V and B be as in Problem 3. Let W = R2 and let T: VW be the linear transformation given by matrix multiplication by the matrix a b 0 c d [88 9] Let D= (d1, d2) where di and d2 H (a) Prove D is a basis of W. (b) Find the matrix for T with respect to the bases B and D.
3. Let V=R3 and let B = (b1, b2, b3), where b₁ = ]. b2 = b3 (a) Prove B is a basis of V over R. (b) For u = 2 find the column vector [u]B. 3 a1 (c) For v = 02 find a formula for the column vector [v]B in terms of a1, a2, a3. аз () 4. Let V and B be as in Problem 3. Let W = R2 and let T: VW be the linear transformation given by matrix multiplication by the matrix a b 0 c d [88 9] Let D= (d1, d2) where di and d2 H (a) Prove D is a basis of W. (b) Find the matrix for T with respect to the bases B and D.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 12E
Related questions
Question
4
![3. Let V=R3 and let B = (b1, b2, b3), where
b₁ =
].
b2 =
b3
(a) Prove B is a basis of V over R.
(b) For u =
2
find the column vector [u]B.
3
a1
(c) For v =
02
find a formula for the column vector [v]B in terms of a1, a2, a3.
аз
() 4. Let V and B be as in Problem 3. Let W = R2 and let T: VW be the linear transformation
given by matrix multiplication by the matrix
a b
0 c d
[88 9]
Let D= (d1, d2) where di
and d2
H
(a) Prove D is a basis of W.
(b) Find the matrix for T with respect to the bases B and D.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30e6ca29-61bc-41d1-bea3-28d53872fdaf%2F18fd6ef6-8ded-4fe9-ae4d-6d292c89a84e%2Fgd4terd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Let V=R3 and let B = (b1, b2, b3), where
b₁ =
].
b2 =
b3
(a) Prove B is a basis of V over R.
(b) For u =
2
find the column vector [u]B.
3
a1
(c) For v =
02
find a formula for the column vector [v]B in terms of a1, a2, a3.
аз
() 4. Let V and B be as in Problem 3. Let W = R2 and let T: VW be the linear transformation
given by matrix multiplication by the matrix
a b
0 c d
[88 9]
Let D= (d1, d2) where di
and d2
H
(a) Prove D is a basis of W.
(b) Find the matrix for T with respect to the bases B and D.
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