For each linear transformation below, state a basis for Range(T) and then indicate if the Range spans the entire codomain.. If you do not need a vector, then place zeros for all entries of that vector (for example, if you only need 2 vectors for the basis, then fill in the first two vectors and make all subsequent vectors have 0 for all boxes). 1) Let T a = la + 1b+2c la + 3b +6c i) A basis for Range(T) would be: la + 2b + 4c] la + 2b +4c] ii) The Range of this transformation spans the entire codomain:
For each linear transformation below, state a basis for Range(T) and then indicate if the Range spans the entire codomain.. If you do not need a vector, then place zeros for all entries of that vector (for example, if you only need 2 vectors for the basis, then fill in the first two vectors and make all subsequent vectors have 0 for all boxes). 1) Let T a = la + 1b+2c la + 3b +6c i) A basis for Range(T) would be: la + 2b + 4c] la + 2b +4c] ii) The Range of this transformation spans the entire codomain:
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 46E
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![For each linear transformation below, state a basis for Range(T) and then indicate if the Range spans the entire codomain.. If you do not need a vector,
then place zeros for all entries of that vector (for example, if you only need 2 vectors for the basis, then fill in the first two vectors and make all
subsequent vectors have 0 for all boxes).
a
13-1
=
1) Let T b
la + 1b+2c
la + 3b +6c
i) A basis for Range(T) would be:
ii) The Range of this transformation spans the entire codomain:
2) Let T(a + bx + cx² + dx³) =
1a + 2b + 4c
1a + 2b + 4c]
i) A basis for Range(T) would be:
la + (-1) b + 1c + 1d
6a+ (-4) b + 8c+5d
ii) The Range of this transformation spans the entire codomain:
2a+ (-1) b + 3c + 1d
9a +(-5) b + 13c + 6d]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdef25b02-21c7-4f0b-87c4-78c9bf8df921%2F8a1a6a0c-5563-421e-8eb9-c7c26cb5c3c3%2F5mpfvx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:For each linear transformation below, state a basis for Range(T) and then indicate if the Range spans the entire codomain.. If you do not need a vector,
then place zeros for all entries of that vector (for example, if you only need 2 vectors for the basis, then fill in the first two vectors and make all
subsequent vectors have 0 for all boxes).
a
13-1
=
1) Let T b
la + 1b+2c
la + 3b +6c
i) A basis for Range(T) would be:
ii) The Range of this transformation spans the entire codomain:
2) Let T(a + bx + cx² + dx³) =
1a + 2b + 4c
1a + 2b + 4c]
i) A basis for Range(T) would be:
la + (-1) b + 1c + 1d
6a+ (-4) b + 8c+5d
ii) The Range of this transformation spans the entire codomain:
2a+ (-1) b + 3c + 1d
9a +(-5) b + 13c + 6d]
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